Question

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?

Answer 1

Adult price is $10 and child is $4.5

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