Select the correct answer.

David opened a coffee shop and sold 60 mochas the first day at [tex]$\$[/tex]2[tex]$ per cup. He wants to increase the price per cup to increase his revenue. He found out that for every $[/tex]\[tex]$0.25$[/tex] increase, [tex]$x$[/tex], 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 [tex]$x$[/tex] times?

A. Multiply [tex]$(60 - 0.25x)$[/tex] and [tex]$(2 + 2x)$[/tex] to create the equation [tex]$y = -0.5x^2 + 119.5x + 120$[/tex].

B. Multiply [tex]$(60 - 2x)$[/tex] and [tex]$(2 + 0.25x)$[/tex] to create the equation [tex]$y = -0.5x^2 + 19x + 120$[/tex].

C. Multiply [tex]$(60 - 0.25x)$[/tex] and [tex]$(2 + 2x)$[/tex] to create the equation [tex]$y = -0.5x^2 + 120.5x + 120$[/tex].

D. Multiply [tex]$(60 - 2x)$[/tex] and [tex]$(2 + 0.25x)$[/tex] to create the equation [tex]$y = -0.5x^2 + 11x + 120$[/tex].



Answer :

To solve the problem, let's break it down step-by-step.

1. Determine the number of cups sold each day:
- Initially, David sold 60 cups per day.
- For each [tex]$0.25 increase in the price, the number of cups sold decreases by 2. - Thus, if the price increases \( x \) times, the decrease in the number of cups sold is \( 2x \). - Therefore, the number of cups sold each day is represented by the expression: \( 60 - 2x \). 2. Determine the price per cup: - Initially, the price per cup is $[/tex]2.
- For each increase, the price per cup goes up by [tex]$0.25. - If the price is increased \( x \) times, the increase in the price is \( 0.25x \). - Therefore, the price per cup after \( x \) increases is represented by the expression: \( 2 + 0.25x \). 3. Calculate the daily revenue: - Revenue is calculated by multiplying the number of cups sold by the price per cup. - Using the expressions from steps 1 and 2, the revenue \( y \) can be represented by: \[ y = (60 - 2x)(2 + 0.25x) \] 4. Simplify the expression to find the equation: - The next step is to simplify the expression \( (60 - 2x)(2 + 0.25x) \). After simplifying, we get the equation: \[ y = -0.5x^2 + 11x + 120 \] Thus, the correct answer is: D. Multiply $[/tex](60-2 x)[tex]$ and $[/tex](2+0.25 x)$ to create the equation [tex]\( y = -0.5 x^2 + 11 x + 120 \)[/tex].