A school will buy x laptops for 450 each and y tablets for... | SAT Linear inequalities in one or two variables Question, Answer Explained

Question bank / Linear inequalities in one or two variables

Math · AlgebraMedium

A school will buy $x$ laptops for $\$450$ each and $y$ tablets for $\$300$ each. It can spend no more than $\$15{,}000$ , and it needs at least $40$ devices in total. Which system of inequalities represents this situation?

A

$450x + 300y \le 15{,}000$ and $x + y \ge 40$

B

$450x + 300y \ge 15{,}000$ and $x + y \le 40$

C

$450x + 300y \le 15{,}000$ and $x + y \le 40$

D

$300x + 450y \le 15{,}000$ and $x + y \ge 40$

Show answer and explanation

Answer: A

The cost is $450x + 300y$ dollars, which can be no more than $\$15{,}000$ : $450x + 300y \le 15{,}000$ . The number of devices, $x + y$ , must be at least $40$ : $x + y \ge 40$ .

Choice C reads at least $40$ devices as no more than $40$ devices.

Why the other choices are wrong

B. Both signs are reversed. The budget is a maximum, and the number of devices is a minimum.
C. At least 40 devices means x + y ≥ 40, not x + y ≤ 40.
D. This switches the prices. Laptops, x, cost $450 each, and tablets, y, cost $300 each.

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