Question

For a Saturday matinee, adult tickets cost $7.50 and kids under 12 pay only $6.00. If 80 tickets are sold for a total of $525, how many of the tickets were adult tickets and how many were sold to kids under 12?

They sold ___ adult tickets and _____ kids tickets.

Answer 1

They sold 30 adult tickets and 50 kids tickets.

Explanation:

This question is solved by a system of equations.

I am going to say that:

x is the number of adult tickets sold

y is the number of kids tickets sold.

80 tickets are sold

This means that
`x + y = 80`, or also,
`x = 80 - y`

For a Saturday matinee, adult tickets cost $7.50 and kids under 12 pay only $6.00. Tickets were sold for a total of $525.

This means that:

`7.5x + 6y = 525`

Since
`x = 80 - y`

`7.5(80 - y) + 6y = 525`

`600 - 7.5y + 6y = 525`

`1.5y = 75`

`y = (75)/(1.5) = 50`

`x = 80 - y = 80 - 50 = 30`

They sold 30 adult tickets and 50 kids tickets.