SAT question 6daf8d70 (Linear Inequalities)

Question

A city employee will plant two types of bushes, azaleas and boxwoods, in a park. There will be no more than $164$ total bushes planted, and the number of azaleas planted will be at most three times the number of boxwoods planted. Which of the following systems of inequalities best represents this situation, where $a$ is the number of azaleas that will be planted, and $b$ is the number of boxwoods that will be planted?

26

Difficulty:Medium

A

$a + b \geq 164$

$3 a \geq b$

B

$a + b \geq 164$

$a \leq 3 b$

C

$a + b \leq 164$

$3 a \geq b$

D

$a + b \leq 164$

$a \leq 3 b$

College Board · Accepted Answer

The correct answer is D. Choice D is correct. It’s given that a city employee will plant azaleas and boxwoods in a park, where a is the number of azaleas that will be planted and b is the number of boxwoods that will be planted. It’s also given that there will be no more than 164 total bushes planted, which can be represented by the inequality a + b ≤ 164 . It’s also given that the number of azaleas planted will be at most three times the number of boxwoods planted, which can be represented by the inequality a ≤ 3 b . Therefore, the system of inequalities containing a + b ≤ 164 and a ≤ 3 b best represents this situation.

Explanation

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Why the other choices are wrong

SAT Question 6daf8d70: Linear Inequalities answer and explanation with Desmos solution

Explanation

Enter in Desmos:

Why the other choices are wrong