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?

Answer 1

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

We know that David wants to increase the price per cup to increase his revenue. He found out that for every $0.25 grows( increase), x, in the price for each cup.

In the event of a price increase, 2 cups remain unsold, and doubling the cups is still not sold. Then the numbers are sold (60-2x). Depending on the choice:

Revenue= (60 -2x)(2 +0.25x)

60·2 +60·0.25x -2x·2 -2x·0.25x

= -0.5x² +11x +120

Answer 2

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

Explanation:

Here, x represents the times at which the price is increased,

Since, the original price of one cup = $ 2,

So, after increasing x times of $ 0.25, the new price of each cup = 2 + 0.25x,

Also, the original number of mochas = 60,

Given,

With increasing the price $ 0.25, x times, the number of cup is decreased by 2 times of x,

That is, the new number of mochas = 60 - 2x

Hence, the total revenue would be,

y = new price of each cup × new number of mochas

⇒ y = (2 + 0.25x)(60 - 2x)

⇒ y = 120 - 4x + 15x - 0.5x²

⇒ y = -0.5x² + 11x + 120

He can find find the equation which represents his daily revenue, by Multiplying (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x² + 11x + 120