SAT question 2c121b25 (Linear Inequalities)

Question

Valentina bought two containers of beads. In the first container $30%$ of the beads are red, and in the second container $70%$ of the beads are red. Together, the containers have at least $400$ red beads. Which inequality shows this relationship, where $x$ is the total number of beads in the first container and $y$ is the total number of beads in the second container?

9

Difficulty:Easy

A

$0.3 x + 0.7 y \geq 400$

B

$0.7 x + 0.3 y \leq 400$

C

$\frac{x}{3} + \frac{y}{7} \leq 400$

D

$30 x + 70 y \geq 400$

College Board · Accepted Answer

The correct answer is A. Choice A is correct. It is given that x is the total number of beads in the first container and that 30% of those beads are red; therefore, the expression 0.3x represents the number of red beads in the first container. It is given that y is the total number of beads in the second container and that 70% of those beads are red; therefore, the expression 0.7y represents the number of red beads in the second container. It is also given that, together, the containers have at least 400 red beads, so the inequality that shows this relationship is 0.3x + 0.7y ≥ 400 .

CookSAT · Answer

Note: x and y are total beads in each container; 30% of x and 70% of y are red, and together they total at least 400.

Explanation

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Why the other choices are wrong

SAT Question 2c121b25: Linear Inequalities answer and explanation with Desmos solution

Explanation

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Why the other choices are wrong