Question

The drama club was selling tickets

to the school play. Adult tickets
cost $8.00 each, and student
tickets cost $5.00 each. The little
theater holds 142 people and was
sold out for both Friday and
Saturday. The total sales for the
two days was $1,948.00.
1. How many adult tickets were
sold out over the two days?
2. How many student tickets were
sold out over the two days?

Answer 1

108 student tickets, and 176 adult tickets were sold

Explanation:

Adult ticket $8 Call the number of adult tickets sold "a"

Student ticket $5 Call the number of student tickets sold "s"

Since we are talking about TWO consecutive days of sold out seats, the total number of seats sold were 2* 142 = 284

Then we create two different equations with the information given:

a + s = 284

8 * a + 5 * s = 1948

we can solve for s in the first equation as follows: s = 284 - a

and use it in the second equation

8 a + 5 (284 - a) = 1948

8 a + 1420 - 5 a = 1948

combining

3 a = 528

a = 528/3

a = 176

we find the number of student tickets using this answer in the substitution equation we used:

s - 284 - 176 = 108

Therefore 108 student tickets, and 176 adult tickets were sold.