# Problem Solving with Linear Models

### Topic Page

Problem Solving with Linear Models### Questions

- How do you use linear models to make predictions?
- How do you find a linear model when given a table of values?
- How do you find a linear model using a graphing calculator?
- What information do you need to create a linear model?
- Do you have a create a scatter plot to write a linear model?
- Question #c42fa
- How do you find three consecutive even integers such that the sum of twice the first and third is 40?
- Tony has twice as much money as Audra. She has $16 less than Karol. Together they have $200. How much money does each have?
- Anthony left home 2 hours before Greg. Both boys were traveling to see their grandmother in New York. Anthony drove at 50 mph and greg drove 65 mph. how long did it take greg to catch up with Anthony?
- Mr. Fairwrench's radiator contains seven quarts of a mixture that is 35% antifreeze and 65% water. He needs a mixture that is 50% antifreeze and 50% water. How many quarts should he drain from his radiator and replace with pure antifreeze?
- How do you find three consecutive even integers such that the product of the first and second is 8 less than the product of 4 and the third?
- Best Buy was having a special in all their tapes and CDs. Jane was able to buy 4 tapes and 3 CDs for $54. Larry bought 6 CDs and 3 tapes for $78. How much did a CD cost on special?
- A mountain climber climbed down a cliff 50 feet at a time. He did this 5 times in one day. What was the overall change in his elevation?
- An ice cream company reported a net profit of $24,000 in 2002 and a net loss of $11,000 in 2003. How much did the company‘s profits change from 2002 to 2003?
- Suppose you write a book. A printer charges $4 per book to print it and you spend $3500 on advertising. You sell the book for $15 a copy. How many copies must you sell so that your income from sales is greater than your total cost?
- After school, Maun'ce walks #1/3# mile to the park and then walks #1/2# mile to his house. How far does Maurice walk from school to his house?
- At the theater, one section of seats has 8 rows with 12 Seats in each row. In the center of each of the first 3 rows are 4 broken seats that cannot be used. How many seats can be used in the section?
- Toby bought a pair of jeans and a sweater. The pair of jeans costs $30 and the sweater costs $35. If the store is having a 25% off sale and Toby has a coupon for an additional 15% off how much did Toby spend in total for the jeans and sweater?
- Mo's farm stand sold a total of 150 pounds of apples and peaches. She sold apples for $2 per pound and peaches for $5 per pound. If she made $350, how many pounds of peaches did she sell?
- Cristiano is saving money to buy a bike that costs $189. He has saved $99 so far. He plans on saving $10 each week. In how many weeks will he have enough money to buy the bike?
- Davey reads 45 pages in an hour. Sally reads 55 pages per hour. If Davey begins to read at 2 PM and Sally starts to read at 2:40 PM, at what time will they be reading the exact same page?
- A coat that usually costs $123 is marked #1/3#. What is the sale price of the coat?
- You have 85 cents made up of nickels (5 cents) and (25 cents). You only have 9 coins. How many quarters and nickels do you have?
- Twice a number decreased by the sum of half the same number and 6 is equal to nine. What is the number?
- There are 20 guests at a party. The host has 8 gallons of punch. He estimates that each guest will drink 2 cups of punch. If his estimate is correct, how much punch will be left over at the end of the party?
- A bag contains 10 pounds of dog food. A family feeds their dogs 0.85 pound of dog food a day. How much dog food is left in the bag after 7 days?
- A scuba diver, hired by an amusement park, collected $119 in nickels, dimes, and quarters at the bottom of a wishing well. There were 300 nickels, and 10 more quarters than dimes. How many quarters and dimes were thrown into the wishing well?
- Parker has quarters and dimes in his piggy bank. He has 4 more dimes than quarters, and he has a total of $7.05 in his bank. How many dimes and quarters does Parker have?
- How do you show that the product of #3# consecutive integers is always divisible by #6# ?
- An express train travels 80 kilometers per hour from Ironton to Wildwood. A local train, traveling at 48 kilometers per hour, takes 2 hours longer for the same trip. How far apart are Ironton and Wildwood?
- An airplane flew 3.5 hours with a 40 mph head wind. The return trip with a tail wind of the same speed took 2.5 hours. How do you find the speed of the plane in still air?
- The concession stand is selling hot dogs and hamburgers during a game. At halftime, they sold a total of 78 hot dogs and hamburgers and brought in $105.50. how many of each item did they sell if hamburgers sold for $1.50 and hot dogs sold for $1.25?
- The sum of two numbers if 67. The smaller number is 3 less than the larger number. What are the 2 numbers?
- There are 2 different jobs jordan is considering. the 1st job will pay her$ 4200 per month plus an annual bonus of $4500. the 2nd job pays $3100 per month plus $600 per month towards her rent and an annual bonus of $500. Which job should she take?
- The perimeter of a rectangle is 66cm and its width is half its length. What are the length and the width of the rectangle?
- A community sponsored a charity square dance where admission was $3 for adults and $1.50 for children. If 168 people attended the dance and the money raised was $432, how many adults and how many children attended the dance?
- Stable High School has a total of 112 boys and girls who play sports. If the number of boys, b is 16 more than twice the number of girls, g, how many boys play sports at this high school?
- The 4200 km trip from new york to san francisco takes 7 h flying against the wind, but only 6 h returning. How do you find the speed of the plane in still air and the wind speed?
- Fred is given a rectangular piece of paper. If the length of Fred's piece of paper is represented by 2x-6 and the width is represented by 3x-5, then the paper has a total area represented by what?
- Mr. White can travel for 6 hours while taking 3 breaks of 10 minutes each. Once, he had to travel for 36 hours. How many minutes in breaks did he take?
- Question #a087f
- If 5 apples sell for $.95, what is the cost of 12 apples?
- You want to make some apple pies. Apples cost $1.40 per pound. How much does it cost to buy 16.2 pounds of apples?
- To make 5 apple pies, you need about 2 pounds of apples. How many pounds of apples do you need to make 20 apple pies?
- Question #201ff
- Question #2a294
- Question #b36cf
- Question #93e34
- The larger of 2 numbers is 11 less than 3 times the smaller. The sum is 69. what are the numbers?
- Question #5ce04
- 8 people meet, and each person shakes every other person's hand once. How many handshakes occurred?
- A machinist creates a washer by drilling a hole through the center of a circular piece of metal. If the piece of metal has a radius of x + 10 and the hole has a radius of x + 6, what is the area of the washer?
- How do you use the prediction equation to predict the missing value?
- Question #af900
- Jane's husband is #2m# tall. The ceiling in their lounge is #2.5m# high and there is a lamp which hangs #41cm# from the ceiling. Will her husband bump his head on the lamp if he walks through the lounge?
- How do you solve #5x - 5= x + 7#?
- Question #3613e
- Question #a35d4
- The larger of 2 numbers is 5 less than 5 times the smaller number. The sum of the two numbers is 61. What are the two numbers?
- Question #a28d2
- If a riding mower costs $300 more than a self-propelled mower and the combined cost of the two mowers is $1100, what is the cost of each mower?
- Question #0b5cb
- Ishi bought a canvas and 8 tubes of paint for $24.95. If the canvas cost $6.95, how much did each tube of paint cost?
- Twelve less than a number is -3. How do you find the number?
- A city known for its temperature extremes started the day at -5 degrees Fahrenheit. The temperature increased by 78 degrees Fahrenheit by midday and then dropped 32 degrees by nightfall. What expression can you write to find the temperature at nightfall?
- What are two consecutive odd positive integers whose product is 323?
- There are 172 South American animals in a zoo. That number is more than #1/2# the number of African animals. If #n# is the number of African animals, what does #n# equal?
- Trevor needs a 93 on his second quiz to have a quiz average of 90. What score did Trevor receive on his first quiz?
- Peyton spent 60% of her money to buy a new television. If the television cost $300, how much money did she have originally?
- Your friend gave you a gift card to a new restaurant. After you spend $36 on dinner there is a balance of $44 left on the gift card. What was the original gift card amount?
- Kelcey is 45. She is also three more than three times Emily's age. How old is Emily?
- How do you solve #-8g + 7= 47#?
- Question #fb041
- On vacation, Charlie and Gail took turns driving. Together they drove 325 miles. The distance Charlie drove was l15 miles more than the distance Gail drove. How far did each of them drive?
- If the difference of two numbers is 43 and the sum of the numbers is 13, what are the numbers?
- Question #74c9b
- The average of 63 and one other number is 33. What's the other number?
- Sara read 81 pages in her book. Colin read 64 pages in his book. How many more pages did Sara read than Colin?
- Question #80bc9
- How do you solve this?
- 2 / 3 of a number is 20 less than a no. Find the number?
- If #p=4xy/(x+y)# then how much is #(p+2x)/(p−2x)+(p+2y)/(p−2y)#?
- Question #d8432
- Question #38513
- Average of 7 numbers is 6.What is 8th no. to be added if the average increases by 10 ?
- The difference of two numbers is 3 and the difference of their square is 69. What are the numbers?
- Question #458d1
- Question #9a993
- There are 172 South American animals in the Springdale Zoo. That is 45 more than half the number of African animals in the zoo. How many African animals are in the zoo?
- Question #5b908
- A certain whole number has the property that appending a digit #5# has the effect of adding #3074#. What is the original number?
- Question #342de
- A small farm has ducks and goats. There are 11 animals in all and 34 legs in all (wings don't count!). How many goats does the farm have? How many ducks?
- Question #7fe4f
- A kite was flying at 20 feet in the air. The wind carried the kite and it is now 32 feet in the air. How many feet did the kite rise?
- Question #34e53
- A textbook publishing company is publishing 10,000 books. Average total costs are $38/book. Average variable costs are $30/book. Marginal cost is $30/book. Sales price of the book is $35. What advice do you have for the company?
- Question #27c5a
- The sum of three consecutive even integers is 312. What are the integers?
- Question #d8842
- Question #3820c
- 2584 divided by 38 equals to?
- One number is three more than the other number. When the square of the smaller number is subtracted from the square of the smaller number, #45# is obtained. What are the two numbers?
- Solve? #x+(x+2)+(x+4)=537#
- An accountant earns $35 for the first hour and $23 for each subsequent hour per client. The accountant charges a client $127. How many hours did they work?
- The sum of two consecutive positive integers and their product is #271#. What are the integers?
- Question #e018a
- Question #1a0d7
- Question #97b73
- How to simplify #3xx(5+7)#?
- The student tickets cost $6.00 less than the general admission tickets. The total amount of money collected for student tickets was $1800 and for general admission tickets, $3000. What was the price of a general admission ticket?
- Question #6a36a
- How do you solve the simultaneous equations #m+n=19# and #m-n=7# ?
- Julio bought tables and chairs for his restaurant. He brought 16 total items and spent $1800. Each table cost $150 and each chair cost $50. How many tables and chairs did he buy?
- Question #98353
- A 70" TV is advertised on sale at a local store. What are the length and width of the television?
- Question #5d8b7
- Question #1f2c9
- If the sum of three consecutive numbers is #-96#, what ids the largest number?
- Question #6a8d7
- You spend $75 to go surfing. It costs $10 per day to rent a surfboard and $15 per day to rent a wetsuit. How many days did you rent the surfboard and wetsuit?
- Question #4cac8
- Question #8ff47
- Question #1afaf
- Question #8f607
- Question #f1ecd
- One integer is 3 more than another. Their product is 70. How do you find the integers?
- The number of seven digit integer is to be formed using only 1, 2 &3 such that the sum of all the digits is 10 . so how many such seven digit number is possible ?
- Question #2f9dc
- The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9 less than three times the original number. What is the original number? Thank you!
- Question #d7550
- Question #e8c24
- How many lawns does he have to landscape to break even?
- Question #df844
- Question #c856b
- If four times a first number is decreased by three times the second number, the result is zero. The sum of the numbers is -7. Find the numbers?
- A collection of quarters and dimes is worth $12.40. There are 76 coins in all. How many of each coin are there?
- Question #82e24
- Nancys sales last week were $140 less than three times Andrea's sales. Together they sold $940. How much did each sell?
- Question #9bdaf
- David works moving lawns and babysitting. He earns $7.10 an hour for mowing and $6.80 an hour for babysitting. How much will he earn for 1 hour of mowing and 5 hours of babysitting?
- The sum of two numbers is 27. The larger number is 6 more than twice the smaller number. What are the numbers?
- Question #16e22
- You buy 3 T-shirts and 2 pairs of shorts for $42.50. Your friend buys 5 T-shirts and 3 pairs of shorts for $67.50. What is the cost of each T-shirt?
- Robert sells 3 packages of cookie dough and 8 packages of pie dough for $35. Phil sells 6 packages of cookie dough and 6 packages of pie dough for $45. How much does each type of dough cost?
- Reggie went to the store. He bought three bags of dog treats for $0.57 each, kitty litter for $2, and four bags of hamster food for $1.38 each. How much money did Reggie give the cashier?
- Question #3b198
- You have a pitcher that holds 39.3 oz of lemonade. If each glass holds 8.8 oz, how many glasses can you completely fill?
- Peter spent an average of $4.50 per day from Monday to Saturday. He spent $5.20 on Sunday. What was the average amount of money he spent per day from Monday to Sunday?
- Paul has a job raking leaves for a neighbor. He makes $7.70 an hour, plus $.45 for each bag he fills. Last Saturday he worked five hours and made a total of $39.85. How many bags of leaves did he fill?
- Question #3dd36
- If three times the difference of the number and #9# is #-3#, what is the number?
- Question #3ef43
- There are 566 members in arts club and 522 are members in the music club. If the total number of people who are members in either or both the clubs is 963, how many people are members in both clubs?
- An airplane flies an altitude of 38,000 feet. As it nears the airport, the plane begins to descent at a rate of 600 feet per minute. At this rate, how many minutes will the plane take to descent to 18,800 feet?
- For a field trip 4 students rode in cars and the rest filled nine buses. How many students were in each bus if 472 students were on the trip?
- The ratio between the present ages of Ram and Rahim is 3:2 respectively. The ratio between the present ages of Rahim and Aman is 5: 2 respectively. What is the ratio between the present ages of Ram and Aman respectively?
- The ages of the three children in a family are as follows: The middle child is one year older than the youngest, while the oldest is three times as old as the youngest. If the sum of their ages is #21# years, what are their ages?
- Question #d3d11
- Question #c7676
- A cruise ship charges $125 per night for a room. There are 250 rooms on the ship. If every room on the ship is booked, how much money does the cruise ship make in a single night?
- Question #65e80
- Question #a83e4
- A number decreased by 30 is the same as 14 minus 3 times the number. What is the number?
- Question #91dff
- How many red fish did fisherman catch?
- Question #f6054
- A bag contains orange blocks and pink blocks. The ratio of orange block to pink blocks is 2 to 11. If 121 pink blocks are in the bag, how many orange blocks are in the bag?
- Question #4770d
- Sue is 7 years older than Bob. Three less than twice Bob's is Sue age, find bob and Sue's ages now?
- Question #b6c11
- Question #89c39
- Question #fd683
- Devon purchased tickets to an air show for 7 adults and 2 children The total cost was $123. The cost of a child's ticket was $6 less than the cost of an adult's ticket. What is the price of an adult and child ticket?
- Question #efac1
- Question #7ddd4
- Question #c7d3a
- Sasha lives 1,493 miles from her grandmother. One year, Sasha's family made 4 round trips to visit her grandmother. How many miles did they travel in all?
- A tape costs $4 less than a CD. Oshkosh bought one CD and five tapes. If the total cost was $70 what was the price of the CD?
- Harvey is 3 times as old as Jane. The sum of their ages is 48 years. What is the age of each?
- Question #c4c31
- Question #3ebcc
- Question #c41bf
- Question #72249
- Question #0efd8
- Question #f7f2c
- Ben has 7 flowers. Tim ha s5 flowers. How many fewer flowers does Tim have than Ben?
- Valencia Theater sold 499 tickets for a play. Tickets cost $14 per student with valid Valencia identification and $23 per none student. If total receipts were $8138, how many Valencia student tickets and none student tickets were sold?
- The attendance at two baseball games on successive nights was 77,000. The attendance on Thursday's game was 7000 more than two-thirds of the attendance at Friday night's game. How many people attended the baseball game each night?
- Question #b318a
- Ben bought 4 pairs of jeans and a T-shirt that cost $8. He had a coupon for $3 off the price of each pair of jeans and spent a total of $92 before tax. What was the price of each pair of jeans?
- One pump can fill a water tank in 40 minutes and another pump takes 30 minutes? How long will it take to fill the water tank if both pumps work together?
- Question #ccbb7
- Question #dd801
- Question #d6e19
- Question #18039
- Question #c7570
- A bucket holds 1 gallon of water. The water is poured into 10 equal-sized containers and there are 54 ounces left. How much does each of the smaller containers hold?
- Doug earns $10.50 per hour working at a restaurant. On Friday, he spent 1.75 hours cleaning, 2.33 hours doing paperwork and 1 hour and 25 minutes serving costumers. What were Doug's earnings?
- 61 is the difference between Carlos's age and 23. How do you write this as an equation?
- A customer went to a garden shop and bought some potting soil for $12.50 and 5 shrubs. If the total bill was $71.00, how much did each shrub cost if they all cost the same?
- Cindy bought 4 lunch specials for $7 each. She gave the cashier $40. How much change should Cindy receive?
- Question #bb227
- How much candy at $1.16 a pound should be mixed with candy worth 86¢ a pound in order to obtain a mixture of 60 pounds of candy worth a dollar a pound?
- A tennis court rental from 9am to 5pm is $3.50 per hour. After 5pm, the rate is $7.00 per hour. Shenice and her friends reserve a tennis court from 3pm to 8pm. What is the total court fees for this period?
- Question #d5d1f
- The Bagel Factory has 12 employees. Eight of them are paid $8.00 an hour, three are paid $10.00 an hour, and the foreman is paid $12.00 an hour. What are the total earnings for one hour?
- Question #71e99
- Question #77db5
- Question #31638
- Question #fcc37
- Question #dfab3
- Question #5f9b6
- The play at the theater charges $7 for adults, $5 for school-age children, and $3 for babies?
- If 16 less than a number is equal to - 19, then what is the number?
- Question #fa62b
- A water hose flow at 5litre a min,how long will it take to fill a 30litres bucket?.
- Question #a915d
- Abraham breeds chickens and ducks. Last month, he sold 50 chickens and 30 ducks for $550. This month, he sold 44 chickens and 36 ducks for $532. How much does each chicken cost? How much does a duck cost?
- If 12 pairs of socks sell for $5.79, how much is one pair of socks?
- Question #eb1b5
- Rolex worked 40 hours last week. He had $74 deducted from his earnings for taxes. If he had $286 left after the deduction, how much does Rolex earn per hour?
- Question #79679
- An online movie streaming plan charges an annual fee of $45 plus $2.50 per movie watched. Another plan has no annual fee but charges $3.75 per movie watched. For how many movies is the cost of the plans the same?
- Lori is 3 times as old as 7 more than Ron’s age. If Ron is a years old, how old is Lori?
- Question #a9c8c
- Question #a0a33
- Question #12d60
- Roberto is dividing his baseball cards equally between himself,his brother,and his 5 friends.Roberto was left with 6 cards.How many cards did Roberto give away?Enter and solve a division equation to solve the problem.Use x for the total number of cards.
- You know your school bus stops at 2 minute intervals the first stop of the route begins at 6:20 AM everyday if your stop is the 18 stop when will the bus arrive for you?
- A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $78. A season ski pass costs $300. The skier would have to rent skis with either pass for $30 per day?
- Sarah is 25 years older than her son Gavin. In ten years, Sarah will be twice Gavin age. How old are Sarah and Gavin?
- Going 40 miles an hour how long would it take me to go 60 miles?
- The average of five consecutive odd integers is -21. What is the least of these integers?
- Twelve less than 4 times a number is 20. What is the number?
- Devaughn is 12 years older than Sydney. The sum of their ages is 64. What is Sydney's age?
- A farmer bought 100 ha of land, part at $1850 per hectare and part at $2250 paying for the whole $215000. How much land was there in each part? Do not round intermediate results. Round only final answers. Round to the whole. ha at $1850/ha ha at
- Lydia has 5 dogs. 2 of the dogs eat 2kg (combined) of food per week. 2 other dogs eat 1kg (combined) per week. The fifth dog eats 1kg of food every three weeks. How much food will the dogs have eaten altogether in 9 weeks?
- Eight less than the product of 6 and a number equals 5. How do I write this as an equation?
- What is the sum of 14 and the product of 8 and a number?
- Bella saw 7 out of 11 people brought a umbrella to the beach there were 99 people. how many of them did not have a beach umbrella?
- How do you write and solve the following? 5 less than the quotient of x and three is two
- Hans needs to rent a moving truck, suppose Company A charges a rate of $40 per day and Company B charges a $60 fee plus $40 per day. For what number of days is the cost the same?
- Cell Phone Company A charges $20 each month plus $0.03 per text. Cell Phone Company B charges $5 each month plus $0.07 per text.Write a system of equations to model the situation using c for cost and t for number of texts. How many texts does a pers??????
- If 5 is added to a number and the sum is tripled, the result is 27 more than than number? Find the number
- A man has 34 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 565 cents, how many dimes and how many quarters does he have?
- The sum of two numbers is 48. One number is 3 times as large as the other. What are the numbers?
- The sum of two numbers is 11 and the diferance is 5? thank you
- The sum of two number is 11 their diffrence is 5. what is the number?
- Again with this!! I need a sum of 2 numbers that equals 20 and they both have a difference of 48, can you please help me? Also, i can't seem to understand this so could you kinda help with that also?
- So if a movie starts at 4:25 and the movie is 1 hour and 25 min long. What time would the movie end ?
- Sharita does a special typing jobs for scientist. she charges $16 for the first 3 pages and $3 for each additional page of scientific typing. sonia, a biologist, paid $106 to have a research paper typed how many pages long was sonia's paper?
- What number is 5 less than half of 32?
- A fair changes an entry fee of $5 and $1.50 to play their games. How much will you need to play 10 games? How many games can you play for $35?
- Two numbers sum to 56. thrice the first subtracted from the second is 4. find the numbers?
- If Emma has 73 assignments but can only do 6 a day how long will it take her to do all 73?