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].
