Question

Daily sales for soccer balls drop by four soccer balls for every $1 increase in price. If the soccer balls were given away, the demand would be 90 soccer balls per day. Which equation represents the demand in daily sales for soccer balls? Let p represent the sales price in dollars.

Answer 1

To represent the demand for soccer balls in terms of price, we can use the information given.

Let \( D \) represent the daily sales (in number of soccer balls), and let \( p \) represent the sales price in dollars.

We know two key pieces of information:
1. When the price is $0 (given away), the demand is 90 soccer balls per day. This gives us a starting point: \( D = 90 \) when \( p = 0 \).
2. The demand decreases by 4 soccer balls for every $1 increase in price. This means that for every unit increase in price \( p \), the demand decreases by 4.

From this information, we can express the relationship between demand \( D \) and price \( p \) with the following linear equation:

\[
D = 90 - 4p
\]

In this equation:
- The term \( 90 \) represents the initial demand when the price is $0.
- The term \( -4p \) accounts for the decrease in demand as the price increases.

Thus, the equation that represents the demand in daily sales for soccer balls is:

\[
D = 90 - 4p
\]