Question the-to

5.1 Linear Inequalities in One or Two Variables - Solving single-variable inequalities
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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?

A.

10t≤75

B.

10+25t≤75

C.

25t≤75

D.

25+10t≤75

The total cost, in dollars, to rent a surfboard consists of a $ 25 service fee

Easy-difficulty · SAT Math · Linear Inequalities in One or Two Variables — Solving single-variable inequalities. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

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+10t 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+10td75 represents this situation.

Choice A is incorrect. This represents a situation where the rental fee, not the total cost, is at most 75 dollars.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.