Question

The middle school and high school bands held an outdoor concert to rasie money for new uniforms. There was a total of 217 people at the concert. Children's tickets cost $1.25 and adult tickets cost $4.50. They collected a total of $710 from the ticket sales. Solve the system you wrote in question #9 above to find the number of each ticket sold.

Answer 1

The number of children's tickets sold is 82 and the number of adult tickets sold is 135.

Step-by-step explanation:

To solve this problem, we can set up a system of equations based on the given information.

Let's assume that the number of children's tickets sold is represented by 'x', and the number of adult tickets sold is represented by 'y'.

From the given information, we know that the total number of tickets sold is 217:

x+ y = 217

We also know that the total amount collected from ticket sales is $710:

1.25x + 4.50y = 710

Now we can solve this system of equations to find the values of 'x' and 'y'.

Multiplying the first equation by 1.25, we get:

1.25x + 1.25y = 271.25

Subtracting equation 3 from equation 2, we can eliminate the 'x' variable:

1.25x + 4.5y - 1.25x - 1.25y = 710 - 271.25

3.25y = 438.75

Dividing both sides of equation 4 by 3.25, we get:

y = 135

Now we can substitute the value of 'y' back into equation 1 to find the value of 'x':

x + 135 = 217

x = 82

Therefore, the number of children's tickets sold is 82 and the number of adult tickets sold is 135.