Question

select the correct answer

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 - 0.25x) ) and ( (2 + 2x) ) to create the equation ( y = -0.5x^2 + 119.5x + 120 )

b. multiply ( (60 - 0.25x) ) and ( (2 + 2x) ) to create the equation ( y = -0.5x^2 + 120.5x + 120 )

c. multiply ( (60 - 2x) ) and ( (2 + 0.25x) ) to create the equation ( y = -0.5x^2 + 10x + 120 )

d. multiply ( (60 - 2x) ) and ( (2 + 0.25x) ) to create the equation ( y = -0.5x^2 + 11x + 120 )

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Explanation:

Step1: Determine price and quantity after x increases

• Price per cup initially: $2. For each $0.25 increase (x times), new price: $2 + 0.25x.
• Quantity sold initially: 60 cups. For each $0.25 increase, quantity decreases by 2 per x increases, so new quantity: 60 - 2x.

Step2: Revenue formula (Price × Quantity)

Revenue \( y = (60 - 2x)(2 + 0.25x) \).

Step3: Expand the product

\[

$$\begin{align*} y&=(60 - 2x)(2 + 0.25x)\\ &=60\times2 + 60\times0.25x - 2x\times2 - 2x\times0.25x\\ &=120 + 15x - 4x - 0.5x^2\\ &=-0.5x^2 + 11x + 120 \end{align*}$$

\]

Answer:

D. Multiply (60 - 2x) and (2 + 0.25x) to create the equation \( y = -0.5x^2 + 11x + 120 \)