Let's calculate the total cost first:
- The customer bought 4 apples at $2 each, so the total cost of apples is 4 * $2 = $8.
- The customer bought 3 oranges at $1.50 each, so the total cost of oranges is 3 * $1.50 = $4.50.
- The customer bought 5 bananas at $0.75 each, so the total cost of bananas is 5 * $0.75 = $3.75.
Now, let's calculate the total number of fruits purchased:
- The customer bought 4 apples + 3 oranges + 5 bananas = 12 fruits.
To find the average price per piece of fruit, we divide the total cost ($8 + $4.50 + $3.75 = $16.25) by the total number of fruits (12):
$16.25 / 12 = $1.3541666666666667 (rounded to $1.35)
Therefore, the average price per piece of fruit the customer purchased is $1.35.