Question

At the movie theater, child admissions is $5.10 and adult admissions is $9.80. On Wednesday, 158 tickets were sold for a total sales of $1,097.20. How many adult tickets were sold that day?

Answer 1

Let the number of adult tickets sold be a and the number of child tickets sold be c.

Since the total number of tickets sold is 158, it follows that:

`a+c=158--------(1)`

Since the total sales is $1,097.20, it follows that:

`9.80a+5.10c=1097.20----(2)`

From equation 1, isolate the variable c:

`c=158-a--------(3)`

Substitute equation 3 into equation 2:

`\begin{gathered} 9.80a+5.10(158-a)=1097.20 \\ 9.80a+805.80-5.10a=1097.20 \\ 9.80a-5.10a=1097.20-805.80 \\ 4.70a=291.40 \\ \text{ Divide both sides of the equation by }4.70: \\ (4.70a)/(4.70)=(291.40)/(4.70) \\ a=62 \end{gathered}`

Therefore, the number of adults is:

62