Question

Adam is planning a pool party to celebrate the last day of school. He wants to give out beach towels to his guests as party favors. Adam ordered 14 beach towels from Sunshine Party Supply. Since this was a bulk order, Sunshine Party Supply reduced the price of each towel by $3.25. Adam paid $105 in all. How much does Sunshine Party Supply normally charge for a beach towel?

Answer 1

Let \( x \) be the normal price of each beach towel.

Since Sunshine Party Supply reduced the price by $3.25 for Adam's bulk order, the reduced price per towel is given by:

\[
x - 3.25
\]

Adam ordered 14 beach towels and paid a total of $105. We can express this situation with the following equation:

\[
14(x - 3.25) = 105
\]

Next, we'll solve this equation for \( x \).

First, divide both sides by 14:

\[
x - 3.25 = \frac{105}{14}
\]

Calculating the division:

\[
\frac{105}{14} = 7.5
\]

Thus, we have:

\[
x - 3.25 = 7.5
\]

Now, add 3.25 to both sides to solve for \( x \):

\[
x = 7.5 + 3.25 = 10.75
\]

Therefore, the normal price of each beach towel is

\[
\boxed{10.75}
\]

To verify, we can check the calculation:

1. The reduced price per towel is:

\[
10.75 - 3.25 = 7.50
\]

2. The total cost for 14 towels at the reduced price:

\[
14 \times 7.50 = 105
\]

The calculations align, confirming that Sunshine Party Supply normally charges \( \boxed{10.75} \) for each beach towel.