a school show had ticket sales of $1,430 the first night and $2,070 the second night. 120 student tickets, 110 adult tickets were sold on the first night. 160 student tickets and 170 adult tickets were sold on the second night. find the price of the student ticket



Answer :

The price of a student ticket is of $5.46.

A equation system is formed when a number of variables are linked and equations are constructed to determine the values of the each variable.

The variables are listed below:

Variable x represents the cost of a student ticket.

Variable y: Adult ticket price.

The formulae are as follows, taking into account the revenues as well as the number of ticket sales:

120x + 110y = $1,430.

160x + 170y = $2,070.

From the second equation:

170y = $2,070 - 160x

y = ($2,070 - 160x) ÷ 170

y = 12.176 - 0.94x

Replacing in the first equation:

120x + 110y = $1,430.

120x + 110(12.176 - 0.94x) = $1,430

120x + 1339.36 - 103.4x = $1,430

16.6x = 90.64

x = 90.64 ÷ 16.6

x = 5.46

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