SAT question e744499e (Linear Inequalities)

Question

An elementary school teacher is ordering $x$ workbooks and $y$ sets of flash cards for a math class. The teacher must order at least $20$ items, but the total cost of the order must not be over $ $80$ . If the workbooks cost $ $3$ each and the flash cards cost $ $4$ per set, which of the following systems of inequalities models this situation?

64

Difficulty:Easy

A

$x + y \geq 20$

$3 x + 4 y \leq 80$

B

$x + y \geq 20$

$3 x + 4 y \geq 80$

C

$3 x + 4 y \leq 20$

$x + y \geq 80$

D

$x + y \leq 20$

$3 x + 4 y \geq 80$

College Board · Accepted Answer

The correct answer is A. Choice A is correct. The total number of workbooks and sets of flash cards ordered is represented by x + y . Since the teacher must order at least 20 items, it must be true that x + y ≥ 20 . Each workbook costs $ 3 ; therefore, 3x represents the cost, in dollars, of x workbooks. Each set of flashcards costs $ 4 ; therefore, 4y represents the cost, in dollars, of y sets of flashcards. It follows that the total cost for x workbooks and y sets of flashcards is 3x + 4y . Since the total cost of the order must not be over $ 80 , it must also be true that 3x + 4y ≤ 80 . Of the choices given, these inequalities are shown only in choice A.

Explanation

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Why the other choices are wrong

SAT Question e744499e: Linear Inequalities answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong