Question

A theater is putting on a play; they sell tickets to children and adults. The ticket prices are $20 for adults and $15 for children. The box office take for the show is $1750 and a total of 92 seats were sold. How many seats were sold to adults and to children? There were tickets for adult seats and tickets for child seats sold.

Answer 1

The number of adults tickets and children ticket/ps sold is; 74 tickets and 18 tickets respectively.

Let

x = adult tickets

x = adult ticketsy = children tickets

• Total seats = 92 seats

• Total revenue = $1,750

• Cost of adults prices = $20

• Cost children = $15

x + y = 92 (1)

20x + 15y = 1,750 (2)

from (1)

• x = 92 - y

substitute x = 92 - y into (2)

• 20x + 15y = 1,750

• 20(92 - y) + 15y = 1,750

• 1840 - 20y + 15y = 1,750

• - 20y + 15y = 1,750 - 1840

• -5y = -90

divide both sides by -5

• y = -90 / -5

• y = 18 tickets

Recall,

• x + y = 92

• x + 18 = 92

• x = 92 - 18

x = 74 tickets

Therefore,

Number of adults tickets sold = 74 tickets and number of children tickets sold = 18 tickets

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