SAT question c50ede6d (Linear Inequalities)

Question

The total cost, in dollars, to rent a surfboard consists of a $ $25$ service fee and a $ $10$ per hour rental fee. A person rents a surfboard for $t$ hours and intends to spend a maximum of $ $75$ to rent the surfboard. Which inequality represents this situation?

53

Difficulty:Easy

A

$10 t \leq 75$

B

$10 + 25 t \leq 75$

C

$25 t \leq 75$

D

$25 + 10 t \leq 75$

College Board · Accepted Answer

The correct answer is D. Choice D is correct. The cost of the rental fee depends on the number of hours the surfboard is rented. Multiplying t hours by 10 dollars per hour yields a rental fee of 10 t dollars. The total cost of the rental consists of the rental fee plus the 25 dollar service fee, which yields a total cost of 25 + 10 t dollars. Since the person intends to spend a maximum of 75 dollars to rent the surfboard, the total cost must be at most 75 dollars. Therefore, the inequality 25 + 10 t ≤ 75 represents this situation.

CookSAT · Answer

Note: The blue cost model stays at or below the green $75 line, so replace x with hours t to match choice D.

Explanation

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Why the other choices are wrong

SAT Question c50ede6d: Linear Inequalities answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong