A company developed a plan to set the selling price of a product. The company determined that for a selling price of 120.00 dollars, zero products would be sold. For each 1.50 dollars decrease in the selling price, the number of products sold would increase by one. For a revenue of exactly 1,966.50 dollars, which of the following could be the number of products sold? (revenue = price × number of products sold)

A company developed a plan to set the selling price of a product. The company determined... | SAT Quadratic functions Practice

Let $n$ = number of products sold.

Each unit sold decreases the price by $1.50$ .
So the price per unit is:
$120 - 1.5n$

Revenue:
$R = n(120 - 1.5n)$

Set revenue equal to $1,966.50$ :
$n(120 - 1.5n) = 1966.5$

$120n - 1.5n^2 = 1966.5$

$1.5n^2 - 120n + 1966.5 = 0$

Multiply through by 2:
$3n^2 - 240n + 3933 = 0$

Divide by 3:
$n^2 - 80n + 1311 = 0$

Discriminant:
$(-80)^2 - 4[1](1311) = 6400 - 5244 = 1156$

$\sqrt{1156} = 34$

$n = \dfrac{80 \pm 34}{2}$

$n = \dfrac{80-34}{2} = 23, \quad n = \dfrac{80+34}{2} = 57$

Only option $23$ is listed.

Answer: A.