Algebraic & Function Expressions

Systems of Equations

5. The sum of 2 numbers is 90. The smaller number is 50 less than the larger number. What is the larger number?

2014 April(71H) Math Question 5

2009 December(68A) Math Question 6

8. Susan makes holiday wreaths for 4 hours every Saturday. It takes her 20 minutes to make a small wreath and 30 minutes to make a large wreath. This Saturday, Susan will make twice as many large wreaths as small wreaths. How many of the large wreaths will she make this Saturday?

2015 April(73G) Math Question 8

9. Andrea manages a company that currently has 116 customers, which is 8 more than twice the number of customers the company had 1 year ago. How many customers did the company have 1 year ago?

2015 June(73C) Math Question 9

11. A system of equations is given below. What is the value of b in the (a,b) solution to the system?

2015 April(73G) Math Question 11

11. Which of the following (x,y) pairs is the solution for the system of equations x + 2y = 2 and −x + y = 7 ?

2021 June(D06) Math Question 11

2011 April(67F) Math Question 13

17. The Tully family and the Quan family ate dinner together at Eugenio's Pasta Restaurant. An order of pasta comes in 1 of 2 sizes, large or small, and consists of 1 of 6 types of pasta and 1 of 5 types of sauce. The table below gives the number of large and small orders of pasta bought by each family, and the price each family paid for their orders of pasta (without tax and tip). The price is the same for each order of a given size. What is the price of a large order of pasta?

2015 December(72E) Math Question 17

2010 December(69A) Math Question 19

2018 December(B05) Math Question 20

20. The product of 2 positive integers is 78. The greater integer is 1 more than twice the lesser integer. What is the greater integer?

2015 April(73G) Math Question 20

21. What is the (x,y) solution, if one exists, to the system of equations y = 2x + 6 and 6x + 12 = 3y ?

Solving pairs of equations

2020 December(D03) Math Question 21

22. A fabric store sells flannel and calico fabrics. Joan pays $25 for 3 yards of flannel and 4 yards of calico. Chris pays $11 for 1 yard of flannel and 2 yards of calico. What is the price of 1 yard of calico?

2017 June(74C) Math Question 22

2009 April(66F) Math Question 22

22. Noah bowled 3 games for his bowling team. In the second game, he scored 10 points more than in the first game; in the third game, he scored 10 points more than in the second game. His average score was 230 points for the 3 games. How many points did Noah score in the third game?

2015 April(73G) Math Question 22

22. At Gussie's Pizzeria, Odetta spends $8.75 (before tax) on the purchase of 2 appetizers and 3 slices of pizza. The price of each slice of pizza is p dollars. The price of each appetizer is twice the price of a slice of pizza. Which of the following systems of equations, when solved, gives the price, a dollars, of an appetizer and the price, p dollars, of a slice of pizza at Gussie's?

2014 December(72G) Math Question 22

23. An ice cream shop sells ice cream cones with exactly 1 of 3 ice cream flavors in the cone. The 3 flavors are vanilla, chocolate, and strawberry. Last Saturday, the shop sold 42 cones. It sold I 1 more with chocolate than with vanilla and 2 more with vanilla than with strawberry. How many cones with strawberry ice cream did the shop sell that Saturday?

2018 April(A09) Math Question 23

2019 June(72F) Math Question 25

2019 April(B04) Math Question 29

2020 June(C02) Math Question 29

30. A construction company builds 3 different models of houses (A, B, and C). They order all the bathtubs, shower stalls, and sinks for the houses from a certain manufacturer. Each model of house contains different numbers of these bathroom fixtures. The tables below give the number of each kind of these fixtures required for each model and the cost to the company, in dollars, of each type of fixture.

2018 June(A11) Math Question 30

31. Consider 3 circles: A, B, and C. The sum of the radii of Circle A and Circle B is 5 m. The sum of the radii of Circle A and Circle C is 8 m. The sum of the radii of Circle B and Circle C is 7 m. What is the length, in meters, of the radius of Circle C ?

System of three equations

2021 April(D05) Math Question 31

2011 June(69F) Math Question 32

35. Nichelle has 84 solid-colored disks that are either red, blue, or green. She lines them up on the floor and finds that there are 24 more red disks than green and 15 more green disks than blue. How many red disks does she have?

2015 December(72E) Math Question 35

36. What is the value of b in the solution of the system of equations below?

2016 April(73E) Math Question 36

37. For every pair of real numbers x and y such that xy = 0 and y = 0, which of the following statements is true?

2018 June(A11) Math Question 37

2011 June(69F) Math Question 37

38. The sum of the measures of LA and LB is 90°. The sum of the measures of LA and LC is 180°. The sum of the measures of LB and ZD is 180°. What is the sum of the measures of LC and ZD ?

2016 December(74H) Math Question 38

40. Let p and q be real numbers such that p + q = 4, —pq = 12, and p > q. What is p?

2015 April(73G) Math Question 40

2009 June(67C) Math Question 41

41. The frequency chart below shows the cumulative number of Ms. Hernandez's science students whose test scores fell within certain score ranges. All test scores are whole numbers.

2017 April(74F) Math Question 41

2019 June(72F) Math Question 44

44. For what value of a would the following system of equations have an infinite number of solutions?

2014 December(72G) Math Question 44

44. Last week, customers bought 5 times as many Style A notebooks as Style C notebooks, and customers bought 2 times as many Style B notebooks as Style C notebooks. Last week, customers bought 392 notebooks. What total amount did customers pay for the 392 notebooks?

2014 April(71H) Math Question 44

46. Given that 3x + 5y = 17 and 2x + 3y = 11, what is the value of x + y ?

2014 April(71H) Math Question 46

46. Susan completed 20 courses in college and her grade point average was 3.15 (A = 4.0 and B = 3.0). If all of her grades were A’s or B’s, and each course grade carried equal weight, what is the number of A’s that Susan received?

2021 April(D05) Math Question 46

2019 April(Z15) Math Question 46

2010 December(69A) Math Question 48

2009 December(68A) Math Question 48

2012 April(70G) Math Question 49

2009 June(67C) Math Question 49

49. For what real number b, if any, will the equation a − 2b + ab = 2 be true for both a = 1 and a = −1 ?

Solve a System of Nonlinear Equations

2021 April(D05) Math Question 49

50. The sum of 2 positive numbers is 151. The lesser number is 19 more than the square root of the greater nunthcr. What is the value of the greater number minus the lesser number?

2017 April(74F) Math Question 50

51. Skyline Tours made $5,000 in 1 day by selling a total
of 30 tickets for Tours A, B, and C. They sold twice as
many tickets for Tour B as for Tour A. How many
tickets were sold for Tour C ?

2019 June(B02) Math Question 51

2012 December(71A) Math Question 51

52. You are given the following system of equations: y = x2 rx + sy t where r, s, and t are integers. For which of the following will there be more than one (x,y) solution, with real-number coordinates, for the system?

2017 April(74F) Math Question 52

2019 April(B04) Math Question 54

2012 June(70C) Math Question 54

2011 June(69F) Math Question 54

55. A sporting-goods store sells baseball caps for $22 each. At this price, 40 caps are sold per week. For every $1 decrease in price, the store will sell 4 more caps per week. The store will adjust the price to maximize revenue. What will be the maximum possible revenue for 1 week?

2017 June(74C) Math Question 55

57. Two numbers have a product of —48 and a sum of 0. What is the lesser of the 2 numbers?

2015 December(72E) Math Question 57

57. The art club designed and made banners of the school colors, blue and white, for their fund-raiser. Each

2017 June(74C) Math Question 57

57. Let a, b, c, and d be real numbers. Given that ac = 1, b+c / d is undefined, and abc = d, which of the following must be true?

Systems of EquationsAlgebraic & Function ExpressionsACT math questions

2014 April(71H) Math Question 5

2009 December(68A) Math Question 6