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