A salesperson earns a base salary of 600 per month plus a... | SAT Linear inequalities in one or two variables Question, Answer Explained

Question bank / Linear inequalities in one or two variables

Math · AlgebraMedium

A salesperson earns a base salary of $\$600$ per month plus a commission of $4\%$ of her total sales for the month. What is the minimum amount of total sales she needs in a month to earn at least $\$2{,}000$ that month?

$\$14{,}000$

$\$35{,}000$

$\$50{,}000$

$\$65{,}000$

Show answer and explanation

Answer: B

Let $s$ be her total sales, in dollars. Her earnings are $600 + 0.04s$ , so $600 + 0.04s \ge 2{,}000$ . Then $0.04s \ge 1{,}400$ and $s \ge 35{,}000$ . She needs at least $\$35{,}000$ in sales.

Choice C divides the full $\$2{,}000$ by $0.04$ , which ignores the $\$600$ base salary.

Why the other choices are wrong

A. This divides 1,400 by 0.1 instead of by 0.04. A 4% commission is 0.04 as a decimal.
C. This divides the full $2,000 by 0.04 and ignores the $600 base salary.
D. This adds the $600 base salary to $2,000 instead of subtracting it.

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