\[ \begin{array}{c}5 \\ s+a=120 \\ 5 s+8 a=750\end{array} \] Maria solved the system and found that 90 student tickets and 30 adult tickets

Let's analyze the given system of equations step by step. The equations provided are: 1. \( s + a = 120 \) (Equation 1) 2. \( 5s + 8a = 750 \) (Equation 2) Where: - \( s \) represents the number of student tickets. - \( a \) represents the number of adult tickets. ### Step 1: Solve for one variable From Equation 1, we can express \( s \) in terms of \( a \): \[ s = 120 - a \] ### Step 2: Substitute into the second equation Now, we substitute \( s \) into Equation 2: \[ 5(120 - a) + 8a = 750 \] ### Step 3: Simplify the equation Distributing the \( 5 \): \[ 600 - 5a + 8a = 750 \] Combine like terms: \[ 600 + 3a = 750 \] ### Step 4: Solve for \( a \) Subtract \( 600 \) from both sides: \[ 3a = 150 \] Now, divide by \( 3 \): \[ a = 50 \] ### Step 5: Substitute back to find \( s \) Now that we have \( a \), we can find \( s \): \[ s = 120 - 50 = 70 \] ### Conclusion The solution to the system of equations is: - \( s = 70 \) (student tickets) - \( a = 50 \) (adult tickets) It seems there was a misunderstanding in the initial claim of 90 student tickets and 30 adult tickets. The correct solution is 70 student tickets and 50 adult tickets.