Question

select the correct answer.

sarah sells fruit trays at a salad shop. last week, she sold 450 fruit trays for $8 per tray. in previous weeks, she found that for every $0.85 increase in the price, she sold 15 fewer fruit trays.

which equation can be used to find sarahs weekly sales income in dollars, \\(y\\), after \\(x\\) price increases of $0.85?

\\(y = -12.75x^2 + 262.5x + 3,600\\)
\\(y = -12.75x^2 + 272.5x + 3,600\\)
\\(y = -12.75x^2 + 502.5x + 3,600\\)
\\(y = -12.75x^2 + 482.5x + 3,600\\)

Explanation:

Express price and quantity

Let \(x\) represent the number of price increases.
The price per tray in dollars is:

$$P(x) = 8 + 0.85x$$

The quantity of trays sold is:

$$Q(x) = 450 - 15x$$

Set up revenue equation

Using the Quadratic Standard Form concept, we define the weekly sales income \(y\) as the product of price and quantity:

$$y = P(x) \cdot Q(x)$$

$$y = (8 + 0.85x)(450 - 15x)$$

Expand the expression

Multiply the binomials:

$$y = 8(450) - 8(15x) + 0.85x(450) - 0.85x(15x)$$

$$y = 3600 - 120x + 382.5x - 12.75x^2$$

Simplify to standard form

Combine the linear terms:

$$-120x + 382.5x = 262.5x$$

Rearrange into standard quadratic form:

$$y = -12.75x^2 + 262.5x + 3,600$$

Answer:

• (A) \(y = -12.75x^2 + 262.5x + 3,600\) (Correct answer)
• (B) \(y = -12.75x^2 + 272.5x + 3,600\)
• (C) \(y = -12.75x^2 + 502.5x + 3,600\)
• (D) \(y = -12.75x^2 + 482.5x + 3,600\)