Question

One night a theater sold 548 movie tickets. An adult's costs $6.50 an child's cost $3.50. In all, $2,881 was takin in. How many of each kind of tickets were sold?

Answer 1

• 321 adult
• 227 child

Explanation:

The fraction of tickets that are adult tickets is ...

((average price per ticket) - (child's ticket cost)) / (difference in ticket costs)

so the fraction of adult tickets is ...

((2881/548) -3.50)/(6.50 -3.50) = 321/548

Then the number of adult tickets is ...

(321/548)·548 = 321

and the number of child tickets is ...

548 -321 = 227

321 adult and 227 child tickets were sold that night.

_____

If you want to write an equation, you can let "a" represent the number of adult tickets sold. Total revenue is ...

6.50a +3.50(548 -a) = 2881

3.00a +1918 = 2881 . . . . . . eliminate parentheses

3a = 963 . . . . . . . . . . . . . . . subtract 1918

a = 321 . . . . . . . . . . . . . . . . . divide by 3

The number of child tickets is ...

548 -a = 548 -321 = 227