Question

A PE teacher bought 4 basketballs and 5 volleyballs for$370.A basketball is $16 more than a volleyball.How much it cost him to buy 5 basketballs and 4 volleyballs?

Answer 1

Let's denote the cost of a volleyball as \( V \) and the cost of a basketball as \( B \).

From the problem, we have the following equations:

1. The total cost of 4 basketballs and 5 volleyballs:
\[
4B + 5V = 370
\]

2. The relationship between the cost of a basketball and a volleyball:
\[
B = V + 16
\]

Now, we can substitute the second equation into the first equation. Substituting \( B \) in the first equation yields:
\[
4(V + 16) + 5V = 370
\]

Expanding this gives us:
\[
4V + 64 + 5V = 370
\]

Combining like terms results in:
\[
9V + 64 = 370
\]

Next, we subtract 64 from both sides:
\[
9V = 370 - 64
\]
\[
9V = 306
\]
\[
V = \frac{306}{9} = 34
\]

Now that we have the cost of a volleyball, we can find the cost of a basketball:
\[
B = V + 16 = 34 + 16 = 50
\]

Now we know the prices:
- Volleyball \( V = 34 \)
- Basketball \( B = 50 \)

Next, we need to find the cost of buying 5 basketballs and 4 volleyballs:
\[
\text{Total Cost} = 5B + 4V
\]

Substituting the known values:
\[
\text{Total Cost} = 5(50) + 4(34)
\]
\[
= 250 + 136
\]
\[
= 386
\]

Thus, the cost to buy 5 basketballs and 4 volleyballs is **$386**.