Let's denote the cost of an adult ticket as \( A \) and the cost of a child ticket as \( C \). According to the information given:
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The total cost of three adult and three child tickets is $75: \[ 3A + 3C = 75 \] Simplifying this, we get: \[ A + C = 25 \quad \text{(1)} \]
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The cost of each child ticket is $3 less than the cost of an adult ticket: \[ C = A - 3 \quad \text{(2)} \]
Now we can substitute equation (2) into equation (1): \[ A + (A - 3) = 25 \] \[ 2A - 3 = 25 \] Adding 3 to both sides, we get: \[ 2A = 28 \] Dividing by 2, we find: \[ A = 14 \]
Now substituting \( A \) back into equation (2) to find \( C \): \[ C = 14 - 3 = 11 \]
Therefore, the price of each adult ticket is $14 and the price of each child ticket is $11.
So the answer is: an adult ticket is $14 and a child ticket is $11.