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The owner of a movie theater was countingthe money from 1 day's ticket sales. He knewthat a total of 150 tickets were sold. Adulttickets cost $7.50 each and children's ticketscost $4.75 each. If the total receipts for theday were $891.25, how many of each kind ofticket were sold?



Answer :

65 adult's ticket and 85 children's ticket was sold

Explanation:

Let the number of tickets for children = x

Let the number of adults ticket = y

Total tickets = 150

x + y = 150 ....equation 1

The cost of tickets per child = $4.75

The cost of tickets per adult = $7.50

Total revenue from tickets = $891.25

Total revenue from tickets = The cost of tickets per child × number of children ticket +

The cost of tickets per adult * number of adults ticket

891.75 = 4.75(x) + 7.5(y)

891.75 = 4.75x + 7.5y ...equation 2

x + y = 150 ....equation 1

891.75 = 4.75x + 7.5y ...equation 2

Using substitution method by making x the subject of formula in equation 1:

x = 150 - y

Substitute for x in equation 2:

891.25 = 4.75(150 - y) + 7.5y

891.25 = 712.5 - 4.75y + 7.5y

891.25 = 712.5 + 2.75y

891.25 - 712.5 = 2.75y

178.75 = 2.75y

y = 178.75/2.75

y = 65

Substitute for x in equation 1:

x + 65 = 150

x = 150 - 65

x = 85

Hence, 65 adult's ticket and 85 children's ticket was sold

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