Word Problems

2 Variable Addition

2009 June(67C) Math Question 1

2009 December(68A) Math Question 3

4. A vending machine only accepts quarters ($0.25) and nickels ($0.05). When the machine was emptied Friday afternoon, 325 coins were counted and had a value of $56.25. Which of the following systems of equations, when solved, gives the number of quarters, q, and the number of nickels, n ?

2013 June(71C) Math Question 4

2010 April(68G) Math Question 4

2020 June(C02) Math Question 4

5. At a grocery store, Jo Ellen received $1.60 when she returned her cans, glass bottles, and plastic bottles. Jo Ellen received $0.05 for each can, $0.10 for each glass bottle, and $0.05 for each plastic bottle. She knew she had returned 6 cans and 8 glass bottles. How many plastic bottles did Jo Ellen return to the store?

2016 April(73E) Math Question 5

6. Gao earns his regular pay of $12 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Gao is paid 1_1_ times his regular pay. How much does Gao earn in a week in
which he works 56 hours?

2021 June(D06) Math Question 6

2009 April(66F) Math Question 7

8. What is the sum of the 4 binomials listed below? x^2 + 2x, 3x + 5, x^2 + 1, 6x — 4

2014 April(71H) Math Question 9

11. Samantha, Nyla, and Jerry own shares of stock in the Triumph Hotels company. The shares of stock that they own have a combined value of $6,880. Samantha owns 70 shares, Nyla owns 50 shares, and Jerry owns 40 shares. What is the value of the shares Samantha owns?

2017 June(74C) Math Question 11

11. At the Winter Weather Store, the price of 1 hat is $12 and the price of 1 scarf is $14. Jovon spent $128 to buy 10 items—a combination of hats and scarves.. How many hats did he buy?

2013 June(71C) Math Question 11

2019 April(Z15) Math Question 12

13. This month, Kami sold 70 figurines in 2 sizes. The large figurines sold for $12 each, and the small figurines sold for $8 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 Kami sell this month?

2014 June(72C) Math Question 13

14. A community theater group performed at 5 local schools. For each school, the table below shows the total number of tickets sold and the total dollar amount collected from ticket sales. At School A, only 2 types of tickets were sold: premium tickets for $10 each and value tickets for $6 each. How many value tickets were sold at School A ?

2018 April(A09) Math Question 14

2010 June(68C) Math Question 17

17. Use the following information to answer questions 17–19. A weeklong summer camp is held in June for children in Grades 3−6. Parents and guardians who enrolled their children for camp by May 15 received a 20% discount off the regular enrollment fee for each child enrolled. For each grade, the table below gives the number of children enrolled by May 15 as well as the regular enrollment fee per child. The grade of any child is that child’s grade in school as of May 15 By May 15, Mr. Ramirez had enrolled his 2 children for camp. One child was in Grade 4, and the other was in Grade 6. What was the total amount Mr. Ramirez paid to enroll his 2 children?

Algebraic Problems

2021 December(E23) Math Question 17

18. At a sandwich shop, customers can order either a meat or a vegetarian sandwich on either white or wheat bread. Out of a total of 50 customers, 20 ordered a sandwich on white bread, 28 ordered a meat sandwich, and 12 ordered a meat sandwich on white bread. The given information is summarized in the table below.

2021 June(D06) Math Question 18

2019 December(C03) Math Question 20

2010 December(69A) Math Question 22

2009 December(68A) Math Question 22

2010 April(68G) Math Question 26

2020 July(C01) Math Question 26

27. Each of 2 identical number cubes, shown below, has a different integer, 1 through 6, on each face. Consider the sample space determined by rolling these number cubes and adding the 2 integers on the faces that land on top. What is the positive difference between the greatest sum and the least sum in this sample space?

2021 June(D06) Math Question 27

2010 December(69A) Math Question 29

2020 June(C02) Math Question 31

32. Ursula will order boxes of red pens and boxes of blue pens for her company. The table below gives the number of pens in each box and the price per box. Ursula will order a total of 50 boxes of pens for a total price of $280. Which of the following systems of equations gives a true relationship between the r boxes of red pens and b boxes of blue pens that Ursula will order?

2 Variable AdditionWord ProblemsACT math questions

2009 June(67C) Math Question 1

2009 December(68A) Math Question 3