Free Compass Math Practice Questions
on Setting up Equations - Answers Included

A set of questions, with answers, on setting up equations similar to the questions in the compass math test, are presented. The answers to the questions are at the bottom of the page and the solutions with full explanations to these questions are also included.

  1. If the length L of a rectangle is 3 meters more than twice its width and its perimeter is 300 meters, which of the following equations could be used to find L?

    A) 3L + 3 = 300
    B) 3L = 300
    C) 3L - 3 = 300
    D) 2L + 3 = 300
    E) 4L = 300

  2. The average of two numbers is 50. Their difference is 40. Write an equation that may be used to find x the smallest of the two numbers.

    A) x - 20 = 50
    B) 2x + 20 = 50
    C) x - 20 = 100
    D) x + 20 = 40
    E) x + 20 = 50

  3. Pump A can fill a tank in 2 hours and pump B can fill the same tank in 3 hours. If t is the time, in hours, that both pump take to fill the tank, which of these equations could be used to find t?

    A) 2t + 3t = 1
    B) t/2 + t/3 = 1
    C) t / (2 + 3) = 1
    D) (2 + 3) / t = 1
    E) t + 2 + 3 = 1

  4. John drove for two hours at the speed of 50 miles per hour (mph) and another x hours at the speed of 55 mph. If the average speed of the entire journey is 53 mph, which of the following could be used to find x?

    A) (55 + x) / 2 = 53
    B) (50 + x) / 2 = 53
    C) (55 + 53) / 2 = x
    D) 100 + 55 x = 53 (2 + x)
    E) 53 x = 2

  5. The sum of 3 consecutive even numbers is 126. Which of these equations could be used to find x, the largest of these 3 numbers?

    A) 3x - 6 = 126
    B) 3x + 6 = 126
    C) 3x + 3 = 126
    D) 3x - 3 = 126
    E) 3x - 9 = 126

  6. The radius of a circle is 3 centimeters (cm) more than twice the side of a square. The circumference of the circle is 4 times the perimeter of the square. Write an equation that can be used to find the radius r of the circle.

    A) 2 pi r = 16 (r - 3)
    B) 2 pi r = 8 (r + 3)
    C) 2 pi r = 16 (r + 3)
    D) 2 pi r = 8 (r - 3)
    E) 6 pi = 4r

  7. The height of a trapezoid is h (mm). b is the length of one of the two bases of the trapezoid and is 2 mm longer than 3 times the length of the second base. The area of the trapezoid is 300 mm2. Write an equation to find b.

    A) (h / 2) (4b - 2) = 300
    B) (h / 2) (4b + 2) = 300
    C) h (4b - 2) = 300
    D) h (4b - 2) = 600
    E) (h / 3) (4b - 2) = 600

  8. 25% of one third of the sum of twice x and 3 is equal to half of the difference of x and its tenth. Write an equation to find x.

    A) 0.25(2x + 3) / 3 = 0.5 (x - 0.1)
    B) 0.25(2x + 3) / 3 = 0.5 (x - 0.1 x)
    C) 0.25(2x) / 3 + 3 = 0.5 (x - 10)
    D) 0.25(2x + 3) / 3 + 3 = 0.5 (x - 10/x)
    E) 0.25(2x) / 3 + 3 = 0.5 (x - 10 x)

  9. The price x of a car was first decreased by 15% and decreased a second time by 10%. Write an equation to find x if the car was bought at $12,000.

    A) (x - 0.15 x) - 0.1 (x - 0.15 x) = 12,000
    B) x - 0.15x - 0.1 x = 12,000
    C) x - 0.15x - 0.1 x = 12,000
    D) (x - 0.15 x) - 0.1 x = 12,000
    E) x = 12,000 - 15% - 10%

  10. A company produces a product for which the variable cost is $6.2 per unit and the fixed costs are $22,000. The company sells the product for $11.45 per unit. Write an equation to find x, the numbers of units sold if the total profit made by the company was $45,000.

    A) 45,000 = 11.45 x + (6.2 x + 22,000)
    B) 45,000 - 22,000 = 11.45 x - 6.2 x
    C) 45,000 = 11.45 x - (6.2 x + 22,000)
    D) 45,000 = 11.45 x - 6.2 x + 22,000
    E) 45,000 + 11.45 x = 6.2 x + 22,000

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