A company models its weekly profit P, in thousands of... | SAT Linear functions Question, Answer Explained

Math · AlgebraHard

A company models its weekly profit $P$ , in thousands of dollars, from selling $x$ hundred units of a product with the function $P(x) = 4.2x - 63$ . According to the model, how many units must the company sell in a week to earn a profit of $\$21{,}000$ ?

$20$

$1{,}500$

$2{,}000$

$20{,}000$

Show answer and explanation

Answer: C

A profit of $\$21{,}000$ is $21$ thousand dollars, so set $P(x) = 21$ : $4.2x - 63 = 21$ . Then $4.2x = 84$ and $x = 20$ . Because $x$ counts hundreds of units, the company must sell $20 \times 100 = 2{,}000$ units.

Choice A is the value of $x$ , which counts hundreds of units, not individual units.

Why the other choices are wrong

A. 20 is the value of x, but x is measured in hundreds of units. The company sells 20 × 100 = 2,000 units.
B. 1,500 units is the break-even point, where P(x) = 0. The question asks for a profit of 21 thousand dollars.
D. This treats x as thousands of units, but x is measured in hundreds.

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