A Store Had a Sale on Art Supplies The Price P of Each Item Was Marked Down 60
Math Models
30 Solve Applications with Linear Inequalities
Learning Objectives
By the end of this section, y'all will exist able to:
- Solve applications with linear inequalities
Before you get started, take this readiness quiz.
- Write as an inequality: ten is at least 30.
If you missed this problem, review (Figure). - Solve
If you missed this problem, review (Effigy).
Solve Applications with Linear Inequalities
Many existent-life situations require us to solve inequalities. In fact, inequality applications are so common that nosotros often do not even realize we are doing algebra. For example, how many gallons of gas can be put in the car for ?20? Is the hire on an apartment affordable? Is in that location plenty time before grade to go become lunch, eat it, and return? How much money should each family member's vacation gift cost without going over budget?
The method we volition use to solve applications with linear inequalities is very much similar the one we used when we solved applications with equations. We volition read the problem and brand sure all the words are understood. Adjacent, we will place what we are looking for and assign a variable to correspond it. We will restate the problem in one sentence to make information technology easy to interpret into an inequality. So, we will solve the inequality.
Emma got a new chore and volition have to move. Her monthly income volition be ?five,265. To qualify to rent an apartment, Emma's monthly income must be at least three times as much every bit the rent. What is the highest rent Emma will authorize for?
Alan is loading a pallet with boxes that each weighs 45 pounds. The pallet tin can safely back up no more than 900 pounds. How many boxes can he safely load onto the pallet?
There tin can exist no more than than twenty boxes.
The elevator in Yehire'southward apartment building has a sign that says the maximum weight is 2,100 pounds. If the average weight of one person is 150 pounds, how many people tin safely ride the elevator?
A maximum of 14 people tin can safely ride in the lift.
Sometimes an application requires the solution to be a whole number, but the algebraic solution to the inequality is not a whole number. In that case, nosotros must round the algebraic solution to a whole number. The context of the awarding will decide whether we circular up or downward. To check applications like this, we will round our reply to a number that is easy to compute with and make sure that number makes the inequality true.
Dawn won a mini-grant of ?4,000 to buy tablet computers for her classroom. The tablets she would like to buy cost ?254.12 each, including revenue enhancement and delivery. What is the maximum number of tablets Dawn tin can buy?
Angie has ?xx to spend on juice boxes for her son'south preschool picnic. Each pack of juice boxes costs ?ii.63. What is the maximum number of packs she can buy?
seven packs
Daniel wants to surprise his girlfriend with a altogether political party at her favorite restaurant. It will cost ?42.75 per person for dinner, including tip and revenue enhancement. His budget for the political party is ?500. What is the maximum number of people Daniel can have at the party?
xi people
Pete works at a computer store. His weekly pay will be either a fixed amount, ?925, or ?500 plus 12% of his full sales. How much should his full sales be for his variable pay option to exceed the fixed amount of ?925?
Tiffany merely graduated from college and her new job will pay her ?xx,000 per year plus ii% of all sales. She wants to earn at least ?100,000 per year. For what total sales will she be able to attain her goal?
at least ?4,000,000
Christian has been offered a new job that pays ?24,000 a year plus iii% of sales. For what total sales would this new job pay more than his current job which pays ?60,000?
at to the lowest degree ?ane,200,000
Sergio and Lizeth have a very tight vacation upkeep. They plan to hire a car from a company that charges ?75 a week plus ?0.25 a mile. How many miles can they travel and nonetheless keep within their ?200 budget?
Taleisha's phone plan costs her ?28.80 a month plus ?0.20 per text message. How many text messages tin she employ and keep her monthly phone neb no more than than ?50?
no more than than 106 text messages
Rameen's heating pecker is ?5.42 per month plus ?1.08 per therm. How many therms can Rameen utilize if he wants his heating beak to be a maximum of ?87.fifty?
no more 76 therms
A common goal of most businesses is to brand a profit. Turn a profit is the money that remains when the expenses have been subtracted from the money earned. In the next example, we will find the number of jobs a modest man of affairs needs to practise every month in order to make a sure amount of profit.
Elliot has a landscape maintenance business organization. His monthly expenses are ?1,100. If he charges ?60 per task, how many jobs must he do to earn a profit of at least ?4,000 a month?
Caleb has a pet sitting business organization. He charges ?32 per hour. His monthly expenses are ?2,272. How many hours must he work in order to earn a profit of at least ?800 per month?
at least 96 hours
Felicity has a calligraphy business concern. She charges ?ii.l per wedding invitation. Her monthly expenses are ?650. How many invitations must she write to earn a turn a profit of at to the lowest degree ?ii,800 per calendar month?
at least 1,380 invitations
Sometimes life gets complicated! There are many situations in which several quantities contribute to the total expense. We must brand certain to account for all the individual expenses when we solve problems like this.
Brenda's all-time friend is having a destination wedding and the consequence will final three days. Brenda has ?500 in savings and can earn ?15 an hour babysitting. She expects to pay ?350 airfare, ?375 for food and entertainment and ?sixty a night for her share of a hotel room. How many hours must she babysit to have plenty money to pay for the trip?
Malik is planning a six-twenty-four hours summer vacation trip. He has ?840 in savings, and he earns ?45 per hour for tutoring. The trip will cost him ?525 for airfare, ?780 for nutrient and sightseeing, and ?95 per nighttime for the hotel. How many hours must he tutor to accept enough coin to pay for the trip?
at least 23 hours
Josue wants to continue a x-solar day road trip next jump. It will cost him ?180 for gas, ?450 for food, and ?49 per night for a motel. He has ?520 in savings and tin earn ?thirty per driveway shoveling snowfall. How many driveways must he shovel to have enough coin to pay for the trip?
at to the lowest degree 20 driveways
Key Concepts
- Solving inequalities
- Read the problem.
- Identify what we are looking for.
- Name what we are looking for. Choose a variable to represent that quantity.
- Interpret. Write a sentence that gives the data to notice information technology. Translate into an inequality.
- Solve the inequality.
- Bank check the respond in the problem and brand sure it makes sense.
- Answer the question with a consummate judgement.
Section Exercises
Exercise Makes Perfect
Solve Applications with Linear Inequalities
In the post-obit exercises, solve.
Mona is planning her son's altogether political party and has a budget of ?285. The Fun Zone charges ?xix per child. How many children tin she have at the party and stay within her budget?
xv children
Carlos is looking at apartments with three of his friends. They want the monthly rent to be no more than ?2360. If the roommates split the hire evenly amongst the iv of them, what is the maximum rent each volition pay?
A water taxi has a maximum load of one,800 pounds. If the average weight of ane person is 150 pounds, how many people tin can safely ride in the water taxi?
12 people
Marcela is registering for her college classes, which cost ?105 per unit. How many units can she take to take a maximum cost of ?1,365?
Arleen got a ?xx gift card for the java shop. Her favorite iced drink costs ?3.79. What is the maximum number of drinks she tin purchase with the gift card?
five drinks
Teegan likes to play golf. He has budgeted ?60 next month for the driving range. Information technology costs him ?10.55 for a bucket of assurance each fourth dimension he goes. What is the maximum number of times he can become to the driving range next calendar month?
Joni sells kitchen aprons online for ?32.50 each. How many aprons must she sell next month if she wants to earn at least ?1,000?
31 aprons
Ryan charges his neighbors ?17.fifty to launder their machine. How many cars must he wash adjacent summer if his goal is to earn at least ?1,500?
Keshad gets paid ?two,400 per calendar month plus 6% of his sales. His blood brother earns ?three,300 per calendar month. For what amount of full sales will Keshad's monthly pay exist higher than his brother's monthly pay?
?15,000
Kimuyen needs to earn ?4,150 per month in order to pay all her expenses. Her chore pays her ?3,475 per month plus iv% of her total sales. What is the minimum Kimuyen's total sales must exist in gild for her to pay all her expenses?
Andre has been offered an entry-level job. The company offered him ?48,000 per twelvemonth plus 3.five% of his total sales. Andre knows that the boilerplate pay for this job is ?62,000. What would Andre's full sales demand to be for his pay to exist at least every bit high every bit the boilerplate pay for this job?
?400,000
Nataly is considering 2 job offers. The first job would pay her ?83,000 per year. The 2nd would pay her ?66,500 plus 15% of her total sales. What would her total sales need to be for her salary on the second offer exist higher than the first?
Jake'due south h2o bill is ?24.lxxx per calendar month plus ?two.twenty per ccf (hundred cubic feet) of h2o. What is the maximum number of ccf Jake can use if he wants his bill to be no more than than ?60?
16 ccf
Kiyoshi'south phone program costs ?17.50 per month plus ?0.15 per text message. What is the maximum number of text letters Kiyoshi tin can use so the phone bill is no more than ?56.50?
Marlon'southward Telly plan costs ?49.99 per calendar month plus ?5.49 per first-run movie. How many offset-run movies tin he watch if he wants to proceed his monthly beak to be a maximum of ?100?
nine movies
Kellen wants to rent a banquet room in a eatery for her cousin's baby shower. The eating house charges ?350 for the banquet room plus ?32.50 per person for lunch. How many people can Kellen accept at the shower if she wants the maximum cost to be ?i,500?
Moshde runs a hairstyling business concern from her house. She charges ?45 for a haircut and style. Her monthly expenses are ?960. She wants to be able to put at least ?1,200 per month into her savings account order to open her ain salon. How many "cut & styles" must she practise to save at least ?1,200 per month?
48 cut & styles
Noe installs and configures software on home computers. He charges ?125 per chore. His monthly expenses are ?1,600. How many jobs must he work in society to brand a profit of at least ?2,400?
Katherine is a personal chef. She charges ?115 per 4-person meal. Her monthly expenses are ?three,150. How many 4-person meals must she sell in society to brand a profit of at least ?ane,900?
44 meals
Melissa makes necklaces and sells them online. She charges ?88 per necklace. Her monthly expenses are ?3745. How many necklaces must she sell if she wants to brand a profit of at to the lowest degree ?one,650?
Five student government officers desire to go to the country convention. It volition cost them ?110 for registration, ?375 for transportation and food, and ?42 per person for the hotel. There is ?450 budgeted for the convention in the student government savings account. They can earn the rest of the coin they need by having a car wash. If they accuse ?five per car, how many cars must they launder in order to have plenty coin to pay for the trip?
49 cars
Cesar is planning a 4-day trip to visit his friend at a college in some other state. It will cost him ?198 for airfare, ?56 for local transportation, and ?45 per mean solar day for food. He has ?189 in savings and tin can earn ?35 for each backyard he mows. How many lawns must he mow to have enough coin to pay for the trip?
Alonzo works every bit a car detailer. He charges ?175 per motorcar. He is planning to move out of his parents' house and rent his first flat. He will need to pay ?120 for awarding fees, ?950 for security eolith, and first and last months' rent at ?1,140 per month. He has ?1,810 in savings. How many cars must he detail to have enough coin to rent the flat?
9 cars
Eun-Kyung works as a tutor and earns ?60 per 60 minutes. She has ?792 in savings. She is planning an anniversary party for her parents. She would like to invite forty guests. The party will cost her ?one,520 for nutrient and drinks and ?150 for the photographer. She volition also have a favor for each of the guests, and each favor will cost ?seven.l. How many hours must she tutor to take enough money for the party?
Everyday Math
Maximum Load on a Phase In 2014, a high school stage collapsed in Fullerton, California, when 250 students got on phase for the finale of a musical product. 2 dozen students were injured. The stage could support a maximum of 12,750 pounds. If the boilerplate weight of a student is assumed to be 140 pounds, what is the maximum number of students who could safely be on the stage?
91 students
Maximum Weight on a Boat In 2004, a water taxi sank in Baltimore harbor and five people drowned. The h2o taxi had a maximum capacity of three,500 pounds (25 people with average weight 140 pounds). The average weight of the 25 people on the water taxi when it sank was 168 pounds per person. What should the maximum number of people of this weight have been?
Wedding Upkeep Adele and Walter plant the perfect venue for their wedding ceremony reception. The cost is ?9,850 for up to 100 guests, plus ?38 for each additional guest. How many guests can attend if Adele and Walter desire the total cost to be no more than ?12,500?
169 guests
Shower Upkeep Penny is planning a babe shower for her daughter-in-law. The eatery charges ?950 for up to 25 guests, plus ?31.95 for each additional guest. How many guests can attend if Penny wants the total cost to be no more than ?one,500?
Writing Exercises
Find your last calendar month'southward phone beak and the hourly salary you are paid at your job. (If you exercise not have a job, use the hourly salary you would realistically exist paid if you had a job.) Calculate the number of hours of work it would have yous to earn at least enough money to pay your phone bill by writing an appropriate inequality and then solving it.
Answers will vary.
Detect out how many units you lot have left, after this term, to achieve your college goal and guess the number of units y'all tin accept each term in college. Calculate the number of terms it will have you to achieve your college goal by writing an appropriate inequality and and so solving it.
Cocky Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ What does this checklist tell yous about your mastery of this section? What steps will you have to improve?
Chapter 3 Review Exercises
three.1 Using a Problem Solving Strategy
Approach Give-and-take Issues with a Positive Attitude
In the following exercises, reflect on your approach to word problems.
How has your attitude towards solving word bug changed as a result of working through this affiliate? Explain.
answers will vary
Did the problem-solving strategy assist yous solve word bug in this chapter? Explain.
Use a Problem-Solving Strategy for Give-and-take Bug
In the post-obit exercises, solve using the trouble-solving strategy for word bug. Call back to write a complete judgement to answer each question.
3-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?
116
At that place are ix saxophone players in the band. The number of saxophone players is 1 less than twice the number of tuba players. Discover the number of tuba players.
Solve Number Problems
In the following exercises, solve each number word problem.
The sum of a number and iii is forty-one. Find the number.
38
Twice the deviation of a number and x is fifty-four. Observe the number.
One number is nine less than another. Their sum is negative twenty-seven. Find the numbers.
Ane number is eleven more than another. If their sum is increased by seventeen, the result is 90. Find the numbers.
One number is two more than four times some other. Their sum is 
Notice the numbers.
The sum of two consecutive integers is 
Discover the numbers.
Find 3 consecutive integers whose sum is 
Discover three consecutive even integers whose sum is 234.
Observe iii consecutive odd integers whose sum is 51.
15, 17, 19
Koji has ?v,502 in his savings account. This is ?xxx less than six times the corporeality in his checking account. How much money does Koji take in his checking account?
3.2 Solve Percent Applications
Translate and Solve Bones Percentage Equations
In the following exercises, translate and solve.
What number is 67% of 250?
167.5
300% of 82 is what number?
12.5% of what number is 20?
160
72 is 30% of what number?
What percentage of 125 is 150?
120%
127.5 is what per centum of 850?
Solve Per centum Applications
In the following exercises, solve.
The bill for Dino's lunch was ?19.45. He wanted to go out 20% of the total nib as a tip. How much should the tip be?
?3.89
Reza was very ill and lost 15% of his original weight. He lost 27 pounds. What was his original weight?
Dolores bought a crib on sale for ?350. The sale price was forty% of the original price. What was the original price of the crib?
?875
Jaden earns ?2,680 per calendar month. He pays ?938 a month for rent. What percent of his monthly pay goes to hire?
Find Percent Increment and Percent Decrease
In the following exercises, solve.
Affections's got a raise in his annual salary from ?55,400 to ?56,785. Find the percent increase.
2.5%
Rowena'south monthly gasoline bill dropped from ?83.75 last calendar month to ?56.95 this month. Find the per centum decrease.
Solve Simple Interest Applications
In the following exercises, solve.
Winston deposited ?3,294 in a bank account with involvement rate two.half dozen%. How much involvement was earned in 5 years?
?428.22
Moira borrowed ?four,500 from her grandfather to pay for her first year of college. Three years afterwards, she repaid the ?iv,500 plus ?243 interest. What was the rate of interest?
Jaime'due south fridge loan statement said he would pay ?one,026 in interest for a 4-twelvemonth loan at 13.5%. How much did Jaime borrow to buy the fridge?
?1,900
In 12 years, a bond that paid half dozen.35% interest earned ?vii,620 interest. What was the primary of the bond?
Solve Applications with Discount or Marker-upwards
In the post-obit exercises, find the sale price.
The original toll of a handbag was ?84. Carole bought information technology on auction for ?21 off.
?63
Marian wants to purchase a coffee table that costs ?495. Next week the java table will be on sale for ?149 off.
In the following exercises, detect ⓐ the amount of discount and ⓑ the sale price.
Emmett bought a pair of shoes on sale at 40% off from an original price of ?138.
ⓐ ?55.twenty ⓑ ?82.80
Anastasia bought a clothes on sale at 75% off from an original price of ?280.
In the following exercises, discover ⓐ the corporeality of disbelieve and ⓑ the discount charge per unit. (Round to the nearest tenth of a percent, if needed.)
Zack bought a printer for his office that was on sale for ?380. The original cost of the printer was ?450.
ⓐ ?lxx ⓑ 15.6%
Lacey bought a pair of boots on sale for ?95. The original toll of the boots was ?200.
In the post-obit exercises, observe ⓐ the amount of the mark-up and ⓑ the list toll.
Nga and Lauren bought a breast at a flea market for ?50. They re-finished it and and so added a 350% mark-up.
ⓐ ?175 ⓑ ?225
Carly bought bottled h2o for ?0.24 per canteen at the disbelieve store. She added a 75% mark-up earlier selling them at the football game.
three.3 Solve Mixture Applications
Solve Money Word Problems
In the following exercises, solve each money word problem.
Francie has ?four.35 in dimes and quarters. The number of dimes is five more the number of quarters. How many of each coin does she have?
xvi dimes, 11 quarters
Scott has ?0.39 in pennies and nickels. The number of pennies is 8 times the number of nickels. How many of each money does he have?
Paulette has ?140 in ?5 and ?x bills. The number of ?ten bills is one less than twice the number of ?5 bills. How many of each does she have?
6 ?5 bills, 11 ?x bills
Lenny has ?3.69 in pennies, dimes, and quarters. The number of pennies is iii more than the number of dimes. The number of quarters is twice the number of dimes. How many of each coin does he take?
Solve Ticket and Stamp Word Problems
In the following exercises, solve each ticket or stamp word problem.
A church luncheon made ?842. Adult tickets cost ?10 each and children'southward tickets cost ?6 each. The number of children was 12 more twice the number of adults. How many of each ticket were sold?
35 adults, 82 children
Tickets for a basketball game game cost ?two for students and ?5 for adults. The number of students was three less than ten times the number of adults. The total amount of money from ticket sales was ?619. How many of each ticket were sold?
125 tickets were sold for the jazz ring concert for a total of ?i,022. Student tickets toll ?6 each and general admission tickets price ?ten each. How many of each kind of ticket were sold?
57 students, 68 adults
1 afternoon the water park sold 525 tickets for a total of ?13,545. Child tickets cost ?nineteen each and adult tickets cost ?forty each. How many of each kind of ticket were sold?
Ana spent ?4.06 buying stamps. The number of ?0.41 stamps she bought was five more the number of ?0.26 stamps. How many of each did she buy?
3 ?0.26 stamps, viii ?0.41 stamps
Yumi spent ?34.15 ownership stamps. The number of ?0.56 stamps she bought was ten less than four times the number of ?0.41 stamps. How many of each did she buy?
Solve Mixture Word Bug
In the post-obit exercises, solve each mixture word problem.
Marquese is making 10 pounds of trail mix from raisins and nuts. Raisins cost ?3.45 per pound and nuts cost ?vii.95 per pound. How many pounds of raisins and how many pounds of nuts should Marquese utilize for the trail mix to price him ?6.96 per pound?
ii.ii lb. of raisins, seven.8 lb. of nuts
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 foursquare feet of tile. She will employ basic tiles that cost ?viii per square foot and decorator tiles that cost ?xx per square foot. How many square anxiety of each tile should she use and so that the overall cost of the backsplash will be ?x per square foot?
Shawn has ?xv,000 to invest. She will put some of it into a fund that pays iv.five% almanac interest and the rest in a document of deposit that pays one.viii% annual interest. How much should she invest in each account if she wants to earn 4.05% annual interest on the total amount?
?12,500 at 4.five%, ?ii,500 at i.8%
Enrique borrowed ?23,500 to buy a car. He pays his uncle 2% involvement on the ?4,500 he borrowed from him, and he pays the banking company 11.v% interest on the rest. What average interest rate does he pay on the full ?23,500? (Circular your reply to the nearest tenth of a percent.)
iii.four Solve Geometry Applications: Triangles, Rectangles and the Pythagorean Theorem
Solve Applications Using Triangle Properties
In the following exercises, solve using triangle properties.
The measures of two angles of a triangle are 22 and 85 degrees. Notice the measure of the third angle.
The playground at a shopping mall is a triangle with perimeter 48 anxiety. The lengths of ii sides are 19 feet and 14 feet. How long is the third side?
A triangular road sign has base of operations 30 inches and elevation 40 inches. What is its area?
600 square inches
What is the pinnacle of a triangle with surface area 67.5 square meters and base ix meters?
One angle of a triangle is 
more the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.
One angle of a right triangle measures 
What is the mensurate of the other angles of the triangle?
The measure of the smallest angle in a correct triangle is 
less than the measure out of the next larger angle. Discover the measures of all 3 angles.
The perimeter of a triangle is 97 feet. One side of the triangle is eleven feet more the smallest side. The tertiary side is half-dozen feet more twice the smallest side. Discover the lengths of all sides.
Use the Pythagorean Theorem
In the following exercises, apply the Pythagorean Theorem to discover the length of the hypotenuse.
26
In the following exercises, utilise the Pythagorean Theorem to find the length of the missing side. Circular to the nearest tenth, if necessary.
8
8.1
In the following exercises, solve. Judge to the nearest 10th, if necessary.
Sergio needs to attach a wire to hold the antenna to the roof of his business firm, equally shown in the figure. The antenna is 8 feet tall and Sergio has 10 feet of wire. How far from the base of the antenna tin can he attach the wire?
Seong is building shelving in his garage. The shelves are 36 inches wide and xv inches tall. He wants to put a diagonal brace beyond the back to stabilize the shelves, every bit shown. How long should the brace be?
Solve Applications Using Rectangle Backdrop
In the post-obit exercises, solve using rectangle backdrop.
The length of a rectangle is 36 feet and the width is 19 feet. Find the ⓐ perimeter ⓑ area.
ⓐ 110 ft. ⓑ 684 sq. ft.
A sidewalk in front of Kathy'south business firm is in the shape of a rectangle 4 feet wide by 45 feet long. Find the ⓐ perimeter ⓑ area.
The surface area of a rectangle is 2356 square meters. The length is 38 meters. What is the width?
62 thousand
The width of a rectangle is 45 centimeters. The surface area is 2,700 square centimeters. What is the length?
The length of a rectangle is 12 cm more than the width. The perimeter is 74 cm. Find the length and the width.
24.5 cm, 12.5 cm
The width of a rectangle is three more than than twice the length. The perimeter is 96 inches. Find the length and the width.
3.5 Solve Uniform Motion Applications
Solve Uniform Move Applications
In the following exercises, solve.
When Gabe drives from Sacramento to Redding information technology takes him 2.2 hours. Information technology takes Elsa two hours to drive the same altitude. Elsa'southward speed is seven miles per hour faster than Gabe's speed. Discover Gabe's speed and Elsa's speed.
Gabe seventy mph, Elsa 77 mph
Louellen and Tracy met at a eating house on the road betwixt Chicago and Nashville. Louellen had left Chicago and drove 3.ii hours towards Nashville. Tracy had left Nashville and drove iv hours towards Chicago, at a speed one mile per hour faster than Louellen'south speed. The distance between Chicago and Nashville is 472 miles. Find Louellen'due south speed and Tracy'southward speed.
Two busses exit Amarillo at the same time. The Albuquerque bus heads w on the I-40 at a speed of 72 miles per hour, and the Oklahoma City bus heads east on the I-forty at a speed of 78 miles per 60 minutes. How many hours will information technology take them to be 375 miles apart?
2.5 hours
Kyle rowed his boat upstream for 50 minutes. Information technology took him 30 minutes to row back downstream. His speed going upstream is two miles per 60 minutes slower than his speed going downstream. Detect Kyle's upstream and downstream speeds.
At half-dozen:xxx, Devon left her house and rode her bicycle on the flat road until seven:30. Then she started riding uphill and rode until 8:00. She rode a total of fifteen miles. Her speed on the flat road was three miles per hour faster than her speed going uphill. Find Devon'south speed on the flat route and riding uphill.
apartment road 11 mph, uphill 8 mph
Anthony drove from New York City to Baltimore, a altitude of 192 miles. He left at 3:45 and had heavy traffic until 5:30. Traffic was calorie-free for the rest of the drive, and he arrived at seven:thirty. His speed in light traffic was four miles per 60 minutes more than twice his speed in heavy traffic. Find Anthony's driving speed in heavy traffic and calorie-free traffic.
iii.half-dozen Solve Applications with Linear Inequalities
Solve Applications with Linear Inequalities
In the following exercises, solve.
Julianne has a weekly food budget of ?231 for her family. If she plans to budget the aforementioned amount for each of the seven days of the calendar week, what is the maximum corporeality she can spend on nutrient each day?
?33 per day
Rogelio paints watercolors. He got a ?100 gift carte du jour to the art supply store and wants to utilise it to buy 
canvases. Each sail costs ?10.99. What is the maximum number of canvases he can buy with his gift card?
Briana has been offered a sales job in another city. The offer was for ?42,500 plus 8% of her full sales. In order to make it worth the move, Briana needs to have an annual salary of at least ?66,500. What would her total sales need to be for her to move?
at least ?300,000
Renee's car costs her ?195 per calendar month plus ?0.09 per mile. How many miles can Renee bulldoze so that her monthly automobile expenses are no more than ?250?
Costa is an auditor. During revenue enhancement season, he charges ?125 to do a elementary tax return. His expenses for ownership software, renting an office, and advertising are ?6,000. How many revenue enhancement returns must he practise if he wants to make a profit of at least ?8,000?
at least 112 jobs
Jenna is planning a 5-day resort vacation with three of her friends. It will cost her ?279 for airfare, ?300 for food and amusement, and ?65 per mean solar day for her share of the hotel. She has ?550 saved towards her vacation and tin can earn ?25 per hour every bit an assistant in her uncle's photography studio. How many hours must she work in lodge to have enough money for her vacation?
Practice Test
Four-fifths of the people on a hike are children. If there are 12 children, what is the total number of people on the hike?
15
One number is iii more than twice another. Their sum is 
Find the numbers.
The sum of two sequent odd integers is 
Find the numbers.
Marla'south breakfast was 525 calories. This was 35% of her total calories for the day. How many calories did she have that twenty-four hours?
Humberto's hourly pay increased from ?16.25 to ?17.55. Detect the pct increase.
viii%
Melinda deposited ?5,985 in a banking concern account with an interest rate of 1.9%. How much involvement was earned in ii years?
Dotty bought a freezer on auction for ?486.50. The original toll of the freezer was ?695. Notice ⓐ the amount of disbelieve and ⓑ the disbelieve charge per unit.
ⓐ ?208.50 ⓑ 30%
Bonita has ?2.95 in dimes and quarters in her pocket. If she has five more dimes than quarters, how many of each coin does she take?
At a concert, ?1,600 in tickets were sold. Adult tickets were ?ix each and children's tickets were ?4 each. If the number of adult tickets was 30 less than twice the number of children's tickets, how many of each kind were sold?
140 adult, 85 children
Kim is making viii gallons of punch from fruit juice and soda. The fruit juice costs ?6.04 per gallon and the soda costs ?four.28 per gallon. How much fruit juice and how much soda should she utilize and so that the dial costs ?five.71 per gallon?
The mensurate of one angle of a triangle is twice the measure of the smallest bending. The measure of the tertiary angle is 14 more than the measure of the smallest angle. Discover the measures of all three angles.
What is the height of a triangle with expanse 277.2 square inches and base 44 inches?
In the following exercises, utilise the Pythagorean Theorem to notice the length of the missing side. Round to the nearest 10th, if necessary.
x
A baseball diamond is really a square with sides of 90 feet. How far is it from home plate to second base of operations, as shown?
127.three ft.
The length of a rectangle is two feet more than five times the width. The perimeter is twoscore feet. Find the dimensions of the rectangle.
Two planes leave Dallas at the same time. One heads e at a speed of 428 miles per hour. The other plane heads west at a speed of 382 miles per 60 minutes. How many hours volition information technology take them to be ii,025 miles apart?
ii.5 hours
Leon drove from his firm in Cincinnati to his sis's firm in Cleveland, a distance of 252 miles. It took him 
hours. For the first one-half hour he had heavy traffic, and the residue of the time his speed was five miles per 60 minutes less than twice his speed in heavy traffic. What was his speed in heavy traffic?
Chloe has a budget of ?800 for costumes for the 18 members of her musical theater group. What is the maximum she can spend for each costume?
at most ?44.44 per costume
Frank plant a rental automobile deal online for ?49 per week plus ?0.24 per mile. How many miles could he drive if he wants the total cost for one week to be no more than ?150?
Source: https://opentextbc.ca/elementaryalgebraopenstax/chapter/solve-applications-with-linear-inequalities/