Let's denote the price of a senior citizen ticket as \( S \) and the price of a child ticket as \( C \). We can set up a system of equations based on the information provided.
From the first day of ticket sales, we know:
- 3 senior citizen tickets and 1 child ticket were sold for a total of $38. This gives us our first equation: \[ 3S + C = 38 \quad \text{(1)} \]
From the second day of sales, we know:
- 3 senior citizen tickets and 2 child tickets were sold for a total of $52. This gives us our second equation: \[ 3S + 2C = 52 \quad \text{(2)} \]
Now we can solve this system of equations. We can start by solving equation (1) for \( C \): \[ C = 38 - 3S \quad \text{(3)} \]
Next, we can substitute equation (3) into equation (2): \[ 3S + 2(38 - 3S) = 52 \]
Now expand and simplify: \[ 3S + 76 - 6S = 52 \] \[ -3S + 76 = 52 \] \[ -3S = 52 - 76 \] \[ -3S = -24 \] \[ S = 8 \]
Now that we have \( S \), we can substitute it back into equation (3) to find \( C \): \[ C = 38 - 3(8) \] \[ C = 38 - 24 \] \[ C = 14 \]
Thus, the price of a senior citizen ticket is $8, and the price of a child ticket is $14.