Questions: Tickets for a dance recital cost 15 for adults and 7 for children. The dance company sold 253 tickets and the total receipts were 2,771. How many adult tickets and how many child tickets were sold?

Solution Steps

To solve this problem, we can set up a system of linear equations. Let \( x \) be the number of adult tickets and \( y \) be the number of child tickets. We have two equations: \( x + y = 253 \) (total tickets) and \( 15x + 7y = 2771 \) (total receipts). We can solve this system using substitution or elimination.

Let \( x \) be the number of adult tickets and \( y \) be the number of child tickets. We have the following equations based on the problem statement:

1. Total tickets: \[ x + y = 253 \]

2. Total receipts: \[ 15x + 7y = 2771 \]

We solve the system of equations to find the values of \( x \) and \( y \).

1. From the first equation: \[ y = 253 - x \]

2. Substitute \( y = 253 - x \) into the second equation: \[ 15x + 7(253 - x) = 2771 \]

3. Simplify and solve for \( x \): \[ 15x + 1771 - 7x = 2771 \] \[ 8x = 1000 \] \[ x = 125 \]

4. Substitute \( x = 125 \) back into \( y = 253 - x \): \[ y = 253 - 125 = 128 \]

Final Answer