12. Admission to the gymnastics meet cost \( \$ 2.40 \) for adults and \( \$ 1.25 \) for students. If 540 tickets were sold for a total of \( \$ 934.90 \), how many tickets of each kind were sold?

Let \( x \) represent the number of adult tickets sold and \( y \) represent the number of student tickets sold. We can set up the following system of equations based on the problem details: 1. The total number of tickets sold: \[ x + y = 540 \] 2. The total revenue from the tickets: \[ 2.40x + 1.25y = 934.90 \] Now we'll solve this system step by step. From the first equation, we can express \( y \) in terms of \( x \): \[ y = 540 - x \] Next, substitute this expression for \( y \) into the second equation: \[ 2.40x + 1.25(540 - x) = 934.90 \] Expanding this gives us: \[ 2.40x + 675 - 1.25x = 934.90 \] Now, combine like terms: \[ (2.40 - 1.25)x + 675 = 934.90 \] \[ 1.15x + 675 = 934.90 \] Next, subtract 675 from both sides: \[ 1.15x = 934.90 - 675 \] \[ 1.15x = 259.90 \] Now, divide by 1.15 to solve for \( x \): \[ x = \frac{259.90}{1.15} \approx 226 \] Now that we have \( x \), we can find \( y \): \[ y = 540 - 226 = 314 \] Thus, the number of adult tickets sold is \( 226 \) and the number of student tickets sold is \( 314 \). In summary: - Adult tickets sold: 226 - Student tickets sold: 314