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At the movie theatre, child admission is 6.30 and adult admission is 9.50 . On Sunday, four times as many adult tickets as child tickets were sold, for a total sales of 1063.20 . How many child tickets were sold that day?
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According to the characteristics of ticket sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.

How many children went to the movie theatre?

In this question we have a word problem, whose information must be translated into algebraic expressions to find a solution. Let be x and y the number of children and adults that went to the movie theatre, respectively.

We need two linear equations, one for the number of people assisting to the theatre and another for the total sales:

x - 4 · y = 0 (1)

6.30 · x + 9.50 · y = 1063.20 (2)

By algebraic procedures the solution to this system is: x = 122.559, y = 30.639. Since the number of tickets sold are integers, then we truncate each result: x = 122, y = 30.

According to the characteristics of ticket sales and the resulting system of linear equations we find that 122 children bought each one a ticket on Sunday.

To learn on systems of linear equations:  

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