Question

At a movie theatre, tickets for children cost $8 each and adult tickets cost $8.75 each. If ticket sales for a group of 35 people totaled $259, how many children were in this group?

Answer 1

Answer:

7 children were in the group

Step-by-step explanation:

Let the number of children's tickets = x

Let the number of adult's tickets = y

we are given the following information:

x + y = 35 - - - - - (1)     (ticket sales for a group of 35 people)

8(x) + 8.75(y) = 259 - - - - - (2)   (totaled $259)

the number of each ticket sold is calculated as follows:

x + y = 35 - - - - - (1)

x = 35 - y - - - - -  (3)

putting the value of x in equation (3) to replace x in equation (2):

8(x) + 8.75(y) = 259 - - - - - (2)

8(35 - y) + 8.75(y) = 259

280 - 8y + 8.75y = 259

280 - 0.75y = 259

280 - 259 = 0.75y

21 = 0.75y

∴ y = 21 ÷ 0.75 = 28

∴ y = 28

putting this value of y into equation 3:

x = 35 - y - - - - -  (3)

x = 35 - 28 = 7

Therefore, 7 children's and 28 adult's tickets were sold, hence 7 children were in the group.