At the movie theatre, child admission is $5.20 and adult admission is $8.50. On Monday, three times as many adult tickets as child tickets were sold, for a total sales of $1043.80. How many child tickets were sold that day?

The Answer is: There are 34 child tickets and 102 adult tickets.

Step-by-step explanation:

Let c = child number of tickets and a = adult number tickets.

The number of child tickets times $5.20 and the number of adult tickets times $8.50 is equal to $1,043.80. See equation below:

5.20c + 8.50a = $1,043.80

There are three times the number of adult tickets as child tickets. Equation below:

a = 3c

By substitution:

5.20c + 8.50a = 1043.80

5.20c + 8.50 (3c) = 1043.80

5.20c + 25.50c = 1043.80

30.7c = 1043.80

c = 1043.80 / 30.7 = 34 child tickets.

Solve for adult tickets:

a = 3c

a = 3 (34) = 102 adult tickets.

Proof:

5.20c + 8.50a = 1043.80

5.20 (34) + 8.50 (102) = 1043.80

176.80 + 867 = 1043.80

1043.80 = 1043.80