SAT question b86123af (Systems of Linear Equations)

Question

Hiro and Sofia purchased shirts and pants from a store. The price of each shirt purchased was the same and the price of each pair of pants purchased was the same. Hiro purchased $4$ shirts and $2$ pairs of pants for $ $86$ , and Sofia purchased $3$ shirts and $5$ pairs of pants for $ $166$ . Which of the following systems of linear equations represents the situation, if $x$ represents the price, in dollars, of each shirt and $y$ represents the price, in dollars, of each pair of pants?

86

Difficulty:Easy

A

$4 x + 2 y = 86$

$3 x + 5 y = 166$

B

$4 x + 3 y = 86$

$2 x + 5 y = 166$

C

$4 x + 2 y = 166$

$3 x + 5 y = 86$

D

$4 x + 3 y = 166$

$2 x + 5 y = 86$

College Board · Accepted Answer

The correct answer is A. Choice A is correct. Hiro purchased 4 shirts and each shirt cost x dollars, so he spent a total of 4x dollars on shirts. Likewise, Hiro purchased 2 pairs of pants, and each pair of pants cost y dollars, so he spent a total of 2y dollars on pants. Therefore, the total amount that Hiro spent was 4x + 2y . Since Hiro spent $ 86 in total, this can be modeled by the equation 4x + 2y = 86 . Using the same reasoning, Sofia bought 3 shirts at x dollars each and 5 pairs of pants at y dollars each, so she spent a total of 3x + 5y dollars on shirts and pants. Since Sofia spent $ 166 in total, this can be modeled by the equation 3x + 5y = 166 .

CookSAT · Answer

Note: The two equations directly translate Hiro’s and Sofia’s purchases into the system that matches choice A.

Explanation

Enter in Desmos:

Why the other choices are wrong

SAT Question b86123af: Systems of Linear Equations answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong