Question

David opened a coffee shop and sold 60 mochas the first day at $2 per cup. He wants to increase the price per cup to increase his revenue. He found out that for every $0.25 increase, x, in the price per cup, the number of cups he sold decreased by 2 per day.

How can David find the equation which represents his daily revenue, in dollars, from mocha sales when the price is increased x times?

A. Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 19x + 120.

B. Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120.

C. Multiply (60 − 0.25x) and (2 + 2x) to create the equation y = -0.5x2 + 119.5x + 120.

D. Multiply (60 − 0.25x) and (2 + 2x) to create the equation y = -0.5x2 + 120.5x + 120.

Answer 1

B. Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120

Explanation:

x is the number of price increases of 0.25 each, so (2 + 0.25x) will be the price after x increases.

2 cups remain unsold for every increase in price, so for x increases, 2x cups remain unsold. Then the number sold is (60 -2x).

Revenue is the product of price and quantity sold, so is ...

... revenue = (60 -2x)(2 +0.25x) . . . . . . matches selections A or B

The product of these binomials is ...

... 60·2 +60·0.25x -2x·2 -2x·0.25x

... = -0.5x² +11x +120 . . . . . . . . . . . . . . . . matches selection B