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:
108 student tickets, and 176 adult tickets were sold
Step-by-step 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.