1. Tickets are being sold for a summer festival at Cynthia Woods Mitchell Pavilion. - Tickets for adults (a) cost \( \$ 8 \) - Tickets for children (c) cost \( \$ 5 \) A total of 55 tickets were sold for a total of \( \$ 365 \). How many of each ticket type were sold? Equations Quantity:

To determine the number of adult and children tickets sold for the summer festival, let's define the variables and set up the corresponding equations based on the given information. ### Variables: - Let \( a \) represent the number of **adult tickets** sold. - Let \( c \) represent the number of **children tickets** sold. ### Given: 1. **Total tickets sold**: \( a + c = 55 \) 2. **Total revenue**: \( 8a + 5c = 365 \) ### Equations: 1. **Quantity Equation**: \[ a + c = 55 \] 2. **Revenue Equation**: \[ 8a + 5c = 365 \] ### Solving the System of Equations: 1. **From the Quantity Equation**, express \( a \) in terms of \( c \): \[ a = 55 - c \] 2. **Substitute** \( a = 55 - c \) into the Revenue Equation: \[ 8(55 - c) + 5c = 365 \] 3. **Expand and Simplify**: \[ 440 - 8c + 5c = 365 \\ 440 - 3c = 365 \] 4. **Solve for \( c \)**: \[ -3c = 365 - 440 \\ -3c = -75 \\ c = \frac{-75}{-3} \\ c = 25 \] 5. **Find \( a \)** using \( a = 55 - c \): \[ a = 55 - 25 \\ a = 30 \] ### Conclusion: - **Adult Tickets Sold**: \( \boxed{30} \) - **Children Tickets Sold**: \( \boxed{25} \)