Word Problems

1 Variable Equations

2013 April(71G) Math Question 1

Five different stores have different prices for a particular brand and style of T-shirts. Those prices are shown in the table below. Which of the 5 stores offers the lowest price for 6 of these T-shirts?

2023 September(G01) Math Question 2

Quinn bought a tractor. He made an initial payment of $900. He then made 36 equal monthly payments. Quinn paid a total amount of $9,000 for the tractor. What was the amount of each of his monthly payments?

2024 December(H31) Math Question 2

2019 June(72F) Math Question 3

3. Olga worked on a project for 4(1/2) hours on each of 6 workdays. On the 7th day of working on the project, Olga worked 1/3 of the time she had worked each of the previous workdays to complete the project. How many hours did it take Olga to complete the project?

Algebraic Problems

2021 April(D05) Math Question 3

2013 December(71E) Math Question 3

3. A 48.5-ounce batch of cologne will be used to fill empty bottles. Each full bottle will contain 0.35 ounces of cologne. This batch of cologne will fill at most how many bottles full of cologne?

2021 December(E23) Math Question 3

What is the cost of 4 4/5 pounds of apples at $1.50 per pound? (Note: No sales tax is charged.)

2023 September(G01) Math Question 3

2009 April(66F) Math Question 4

A company reimburses its employees for use of a personal vehicle for company travel at the rate of $10.00 per day plus $0.445 per mile. Jorge, an employee of the company, traveled exactly 120 miles on Monday and exactly 100 miles on Tuesday using his personal vehicle for company travel. For these 2 days, what was the amount of Jorge's reimbursement?

35 February(Z14) Math Question 4

4. Of the 200 parking spaces in a parking lot, 6% of the\ spaces are reserved for handicapped parking. Of those parking spaces NOT reserved for handicapped parking, 20 are suitable for compact cars only. How man spaces that are NOT reserved for handicapped parking are suitable for noncompact cars?

2021 December(E23) Math Question 4

2009 June(67C) Math Question 5

Ana plans to save $200 for a summer skate park pass. She already has $45 and plans to save $15 per week. At this rate of savings, what is the minimum number of weeks after which Ana will have enough money for the skate park pass?

2025 October(J08) Math Question 5

A city bus picks up and drops off passengers according to the table below. The bus has 0 passengers before Stop 1. After Stop 5, there are 13 passengers remaining on the bus. How many passengers did the bus pick up at Stop 1?

2024 September(H11) Math Question 5

2019 December(C03) Math Question 6

Before opening her lemonade stand, Haley purchased lemonade mix for $2.30 and a package of cups for $1.50. Haley sells each cup of lemonade for $0.50. Which of the following expressions gives Haley's total profit, in dollars, from selling x cups of lemonade?

35 February(Z14) Math Question 6

Fred's cell phone service costs $25.00 per month and includes 100 minutes. For any minutes used after the 100 minutes, he is charged $0.10 per minute. Fred has budgeted $33.00 per month for his cell phone service. What is the maximum number of minutes Fred could use in 1 month without exceeding his budget?

2024 June(G20) Math Question 6

6. Of the 180 students in a college course, 1/4 of the students earned an A for the course, 1/3 of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?

Ratios

2021 April(Z04) Math Question 6

7. Fifty shoppers at a pet store were asked if they owned at least 1 cat or at least 1 dog. Data from their answers were recorded below. How many of these shoppers said that they owned NEITHER a cat NOR a dog?

Venn diagrams

2021 April(D05) Math Question 7

2018 December(B05) Math Question 7

7. Tawanna bought a used car. She made an initial payment of $700.00. She then made 36 equal monthly payments. The total amount Tawanna paid for the car was $7,000.00. What was the amount of each of her monthly payments?

2021 December(E23) Math Question 7

The Sheffield High School girls' softball team currently has a record of 11 wins, 8 losses, and 0 ties. What is the least number of its remaining 14 games the team must win to finish the season winning more than 50% of all the team's games?

35 February(Z14) Math Question 8

2012 December(71A) Math Question 9

9. Lyle and Ming are painting an art room. They started with 4 gallons of paint. On the first day, Lyle used gallon of paint and Ming used 1 gallons of paint. How many gallons of paint were left when they completed their first day of painting?

Fractions

2021 December(E23) Math Question 9

Chris can paint 1/6 of a fence per hour. Sandy can paint 1/8 of the same fence per hour. What fraction of the fence will be painted when Chris and Sandy work at these rates for 2 hours?

2023 September(G01) Math Question 9

Zhu has $25 to spend on camping supplies. The table below shows the prices, including tax, of some items. Given that Zhu buys 1 hand broom, 1 rubber mallet, and 2 telescoping forks, what is the greatest number of tent stakes she can buy with her remaining money?

2024 December(H31) Math Question 9

On the first day of school, Mr. Thibodeaux gave his third-grade students 9 new spelling words to learn. On each day of school after that, he gave the students 6 new spelling words. How many new spelling words had he given the students by the end of the 30th day of school?

2024 April(Z13) Math Question 10

11. Marietta purchased a car that had a purchase price of $10,400, which included all other costs and tax. She paid $2,000 as a down payment and got a loan for the rest of the purchase price. Marietta paid off the loan by making 48 payments of $225 each. The total of all her payments, including the down payment, was how much more than the car's purchase price?

2016 April(73E) Math Question 11

Jerrica drives to and from school once per day in a car that travels 20 miles on 1 gallon of gas. A trip from Jerrica's house to school and back is 6 miles. Gas costs $5 per gallon. Suppose Jerrica rides her bike to and from school for 10 school days. How much money will Jerrica save on gas by not driving to and from school those days?

35 February(Z14) Math Question 11

12. Carrie's Chocolate Shop and Tamika's Treat Shop both sell candy in boxes. The table below lists the price (the total amount the customer pays) of each box of candy sold at the shops. For each shop, there is a linear relationship between the price of a box of candies and the number of candies in that box. These are the only numbers of candies that can be purchased at the shops. Jeremy has $10.00 in quarters to spend on candy. What is the maximum number of quarters he would have left after paying for a box of 25 candies at Tamika's Treat Shop? (Note: Each quarter is worth $0.25.)

2015 June(73C) Math Question 12

2013 April(71G) Math Question 13

2012 December(71A) Math Question 13

This month, Reed sold 40 figurines in 2 sizes. The large figurines sold for $12 each, and the small figurines sold for $4 each. The amount of money he received from the sales of the large figurines was equal to the amount of money he received from the sales of the small figurines. How many large figurines did Reed sell this month?

2024 September(H11) Math Question 13

2012 June(70C) Math Question 14

Each ticket for the track meet had a price of $8. Tickets were sold for exactly 85% of the stadium's capacity. How many dollars did SHS collect through ticket sales for this meet?

35 February(Z14) Math Question 15

The Student Council is preparing a budget for an upcoming fund-raising dance. They have decided to spend $150 for a light and sound show, $400 for refreshments, and $50 for decorations. These are the only expenses. Given that the Student Council estimates 500 students will attend the dance, what should be the price, per student, for admission to the dance if the Student Council wants to raise as close as possible to $300 after paying expenses?

2024 April(Z13) Math Question 15

The Cross High School girls' softball team currently has a record of 14 wins, 11 losses, and 0 ties. What is the least number of its remaining 12 games the team must win to finish the season winning more than 50% of all the team's games?

2024 September(H11) Math Question 15

2010 April(68G) Math Question 17

In Amul's yard, there was no snow on the ground at 10:15 a.m. From 10:15 a.m. until 3:30 p.m., it snowed at an average rate of 1/2 inch per hour. How many inches of snow were on the ground at 3:30 p.m.?

2023 April(F11) Math Question 17

18. Maurice earns $12.50 per hour for the first 40 hours he works each week. For each hour beyond 40 that he works in 1 week, Maurice earns $18.75 per hour. Last week Maurice earned $931.25. How many hours did Maurice work last week?

2014 April(71H) Math Question 18

19. The Tully family also bought 5 salads priced at $2.00 per salad and 12 breadsticks priced at $1.50 for an order of 3 breadsticks. What was the total price of the pasta, salads, and breadsticks the Tully family bought, without tax and tip?

2015 December(72E) Math Question 19

Marcy is making toys to sell at the local school fair. Each toy costs Marcy $2.25 to make, and she will sell them for $4.05 each. What is the minimum number of toys she can make and sell to earn a profit of at least $81.00?

2024 June(G20) Math Question 20

21. The total cost, c dollars, for Main Street Orchestra to perform a concert at Milly's Auditorium is determined by c = r + 20m, where r is the rental fee, in dollars, of the auditorium and m is the number of orchestra members playing. The Friday night rental fee for Milly's Auditorium is $500. There will be 30 orchestra members playing in Friday night's concert. For the total price of exactly 200 tickets to equal the total cost of performing the concert, what should be the price of each ticket?

2015 December(72E) Math Question 21

Kate could not build the snowman until there was 6 inches of snow on the ground. At how many hours after 8:00 a.m. yesterday was there exactly 6 inches of snow on the ground?

2024 April(Z13) Math Question 21

One watch gains 2 1/2 minutes per hour while another watch loses 1 1/4 minutes per hour. If both watches are set correctly at noon, after how many hours will the times shown by the watches be exactly 1 hour apart?

2024 April(Z13) Math Question 25

26. For which night was the total amount collected for the tickets greater, and by how many dollars was it greater?

2014 December(72G) Math Question 26

27. Alani works 8 hours per day 5 days each week at a custom embroidery shop. Each day Alani is paid either $1.00 per shirt that she stitches or $10.00 per hour, whichever daily amount is higher. Alani stitched the following numbers of shirts: 60 on Monday, 52 on Tuesday, 85 on Wednesday, 80 on Thursday, and 90 on Friday. What is Alani’s total pay for these 5 days?

2018 April(A09) Math Question 27

28. Among a group of 20 students, 13 students are members of the Math Club, 11 students are members of the Drama Club, and 9 students are members of both clubs. How many of the 20 students are NOT members of either club?

2021 December(E23) Math Question 28

Jared is driving home. He is currently 231 miles away from home. His car's fuel tank holds 16 gallons and is 3/4 full of fuel. Given that his car travels 22 miles per gallon of fuel and he doesn't stop for fuel, how many gallons of fuel will be in his tank when he gets home?

2024 September(H11) Math Question 28

28. Bo and Tia will balance perfectly on the seesaw shown below if w1 × d1 = w2 × d2, where w1 and d1 are the weight of Bo and his distance from the fulcrum, respectively, and w2 and d2 are similarly defined for Tia. Bo weighs 60 pounds and is sitting 3(1/2) feet from the fulcrum. Tia weighs 2/3 Bo’s weight. What distance, in feet, from the fulcrum must Tia sit in order for Bo and Tia to balance perfectly on the seesaw?

2021 April(D05) Math Question 28

Jerry will purchase 42 cubic feet of gravel for his patio. The local rock quarry will sell gravel in the exact volume needed by the customer. What is the cost, in dollars, to purchase the gravel from the local rock quarry?

35 February(Z14) Math Question 29

What is the positive difference between the given values of average distance from the Sun for Mars and for Mercury?

2023 April(F11) Math Question 30

32. Shefali goes to a farmers’ market every Saturday. Two Saturdays ago, Shefali purchased 3 apples and 4 oranges for a total of $3.47. Last Saturday, she purchased 12 oranges, but no apples, and spent $6.36. Today, she only has one $10 bill. Given that none of the prices have changed over the last 3 weeks, what is the maximum number of apples she can purchase today? (Note: No sales tax is charged at this farmers’ market.)

2021 December(E23) Math Question 32

34. A family will rent a picnic shelter for $200 for a reunion. The cost of the shelter will be distributed equally among the people who plan to attend. The current cost per person will decrease by $1 if 10 more people plan to attend the reunion. How many people are currently planning to attend the reunion?

2016 April(73E) Math Question 34

36. Mrs. Smith will install a ceiling fan in each room of the cabin and will place curtains over the 4 windows. Each of the ceiling fang has a price of $52.00. The price of curtains for each small window (S) is $39.50, and the price of curtains for the large window (L) is twice that for the small window. Based on this information, which of the following values is closest to the total price Mrs. Smith will pay for curtains and ceiling fans?

2017 April(74F) Math Question 36

37. For how many volunteers did the Sam77  test give an incorrect result?

2021 April(Z04) Math Question 37

Julia will serve grape juice from 12-ounce cans at her graduation party. She already has 3 boxes that each contain 12 such cans. How many more 12-ounce cans of grape juice does Julia need to have exactly enough juice to serve 60 guests 8 ounces each?

2023 April(F11) Math Question 37

The Chocolate Mousse Lodge sells gift boxes of chocolates. The actual cardboard box is free, and there is a fixed cost for each gourmet chocolate and another fixed cost for each premiere chocolate in each gift box. A gift box with 5 gourmet chocolates and 10 premiere chocolates costs $30.35, and a gift box with 6 gourmet chocolates and 6 premiere chocolates costs $22.68. What is the cost of a gift box with 2 gourmet chocolates and 1 premiere chocolate?

2024 December(H31) Math Question 38

2012 April(70G) Math Question 39

You have a piece of lumber that is exactly 8 feet long. You cut it into 3 pieces: one is exactly 3 feet 6 inches long and another is exactly 2 feet 3 inches long, as shown below. If each cut is exactly 1/8 inch wide, how long, in feet and inches, is the third piece?

2024 April(Z13) Math Question 40

2018 December(B05) Math Question 44

The cost of a certain type of carpet is $10 per square yard. What would be the cost of carpet of this type to cover a rectangular floor 12 feet by 18 feet?

35 February(Z14) Math Question 45

2019 June(72F) Math Question 47

2013 April(71G) Math Question 49

Craig writes a check for $18. When he records the check in his check register, he accidentally adds $18 to his balance instead of subtracting $18, which causes a discrepancy between what Craig's check register shows and what it should show. Because of his mistake, Craig's check register shows:

1 Variable EquationsWord ProblemsACT math questions

2013 April(71G) Math Question 1

2023 September(G01) Math Question 2