Question

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 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:
\[
y = (8 + 0.85x)(450 - 15x)
\]