SAT question 84d0d07e (Linear Inequalities)

Question

A clothing store is having a sale on shirts and pants. During the sale, the cost of each shirt is $ $15$ and the cost of each pair of pants is $ $25$ . Geoff can spend at most $ $120$ at the store. If Geoff buys $s$ shirts and $p$ pairs of pants, which of the following must be true?

34

Difficulty:Easy

A

$15 s + 25 p \leq 120$

B

$15 s + 25 p \geq 120$

C

$25 s + 15 p \leq 120$

D

$25 s + 15 p \geq 120$

College Board · Accepted Answer

The correct answer is A. Choice A is correct. Since the cost of each shirt is $ 15 and Geoff buys s shirts, the expression 15 s represents the amount Geoff spends on shirts. Since the cost of each pair of pants is $ 25 and Geoff buys p pairs of pants, the expression 25 p represents the amount Geoff spends on pants. Therefore, the sum 15 s + 25 p represents the total amount Geoff spends at the store. Since Geoff can spend at most $ 120 at the store, the total amount he spends must be less than or equal to 120 . Thus, 15 s + 25 p ≤ 120 .

CookSAT · Answer

Note: The inequality 15x + 25y ≤ 120 directly models the total cost of x shirts at 15 each and y pants at 25 each, with the total being at most $120.

Explanation

Enter in Desmos:

Why the other choices are wrong

SAT Question 84d0d07e: Linear Inequalities answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong