ACT Math Practice Question: Algebra & Inequalities

Eloise is a car salesperson who makes a minimum base pay of $2,500 per month or 8% commission on her monthly sales, whichever is more. If x = Eloise’s monthly sales, which expression most accurately describes x when she makes more than her minimum base pay in a month?

A. x > 31250
B. x ≥ 31250
C. x ≤ 32150
D. x > 2500
E. x ≤ 2500

 

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Eloise is a car salesperson who makes a minimum base pay of $2,500 per month or 8% commission on her monthly sales, whichever is more. If x = Eloise’s monthly sales, which expression most accurately describes x when she makes more than her minimum base pay in a month?

A. x > 31250
B. x ≥ 31250
C. x ≤ 32150
D. x > 2500
E. x ≤ 2500

The correct answer is A. Express the equation algebraically as an inequality. Convert 8% to a decimal: 8/100 = 0.08
2500 < 0.08x
Divide both sides by 0.08
31250 < x

x  > 31250

Note that it is incorrect to use the ≥ symbol because if she earns exactly $31,250 in monthly of sales, then her commission is exactly 3,1250 • 0.08 = 2,500, and the question asks you to describe x when she makes more than her minimum base pay in a month.

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