SAT Linear inequalities in one or two variables Practice Question 17 (Hard)

Question bank / Linear inequalities in one or two variables

Math · AlgebraHard

A store sells shirts for $\$12$ each and hats for $\$8$ each. A customer wants to buy at least $10$ items and spend no more than $\$100$ . What is the maximum number of shirts the customer can buy?

$5$

$6$

$8$

$10$

Show answer and explanation

Answer: A

Let $s$ be shirts and $h$ hats: $s + h \ge 10$ and $12s + 8h \le 100$ . To maximize shirts, buy the fewest hats possible, $h = 10 - s$ . Then $12s + 8(10 - s) \le 100$ , so $4s + 80 \le 100$ and $s \le 5$ . Five shirts and five hats cost exactly $\$100$ .

Choice C is the most shirts the customer could afford with no hats, but then the customer would buy only 8 items, not at least 10.

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