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.

Question

Which equation can be used to find Sarah's weekly sales income in dollars, y, after x price increases of $0.85?

Answer 1

To determine Sarah's weekly sales income \( y \) after \( x \) price increases of \( 0.85 \), we can analyze the relationship between the price of fruit trays, the quantity sold, and the sales income.

1. Initial conditions:

   • Initial price per tray = \( 8 \) dollars
   • Initial quantity sold = \( 450 \) trays

2. Price increase: For each increase of \( 0.85 \), the new price after \( x \) increases would be: \[ \text{New price} = 8 + 0.85x \]

3. Quantity sold: For each increase of \( 0.85 \), she sells 15 fewer trays. Thus, the quantity sold after \( x \) increases would be: \[ \text{New quantity sold} = 450 - 15x \]

4. Sales income: The sales income \( y \) can be calculated as the product of the new price and the new quantity sold: \[ y = (\text{New price}) \times (\text{New quantity sold}) = (8 + 0.85x)(450 - 15x) \]

Thus, the equation that can be used to find Sarah's weekly sales income in dollars \( y \) after \( x \) price increases of \( 0.85 \) is: \[ y = (8 + 0.85x)(450 - 15x) \]