At the movie theatre, child admission is $5.20 and adult admission is $9.40. On Wednesday, 122 tickets were sold for a total sales of $911.60. How many child tickets were sold that day?

Answer 1

Let C = #of child tickets sold

A = # adult tickets sold

Then one equation is:

A + C = 122 (total number of tickets sold is 122).

Now let's use the cost of each ticket to generate the total revenue.

If A tickets are sold at $9.40 each, then the money brought in by A adults is 9.4 A.

Similarly for C each ticket generates $5.20 so revenue there is 5.2C.

Add those revenues to get the total:

9.4 A + 5.2 C = 911.6

Suggestion: multiply every term by 10 to clear the decimals:

94A + 52C = 9116

Solve the very 1st equation for A (or C) and substitute into that last equation.

C = 122 - A

Substitute:

94A + 52(122 - A) = 9116

94A + 52(122) - 52A = 9116

42A + 52(122) = 9116

42 A = 9116 - 52(122)

A = [9116 - 52(122)]/42

A = 66 (confession: I used a calculator)

Find C by substituting 66 for A:

C = 122 - A

C = 122 - 66

C = 56

Check: 66($9.40) + 56($5.20) = $911.60