21) Diana's school is selling tickets to their fall musical.

They sold 3 adult tickets and 8 children's tickets and made $66.

The next day they sold 8 adult tickets and 15 children's tickets

and took in$147.50. What is the price each of one adult ticket

and one child ticket?

Adult price is $10 and child is $4.5

Step-by-step explanation:

In this case we can solve it using a 2x2 system of equations, like this:

let x: price of adult tickets

let y: price of children tickets

So:

3*x + 8*y = 66

8*x + 15*y = 147.5 = > x = (147.5 - 15*y) / 8

Replacing, we are left with that:

3 * ((147.5 - 15*y) / 8) + 8*y = 66

55.3125 - 5.625 * y + 8 * y = 66

8 * y - 5.625 * y = 66 - 55.3125

2.375 * y = 10.6875

y = 10.6875/2.375

y = 4.5

Now to calculate x:

x = (147.5 - 15*4.5) / 8

x = 10

which means the adult price is $10 and the child is $4.5