Beth’s school is selling tickets to a fall musical. On the first day of ticket sales. The school sold 12 senior tickets and 16 child tickets for a total of $336. The school took in $312 on the second day by selling 15 senior tickets and 11 child tickets. Find the price of a senior ticket and the price of a child ticket.

To find the linear equation of two variables we need to multiply the value of one variable to appropriate number to become similar in x or y. Then from excluding one variable we find the value of other. at last putting value in any of the given linear equation to find the next term.

Let the price of senior ticket is x and child ticket is y

Given, senior ticket = [tex]12[/tex] and child ticket = [tex]16[/tex] of $[tex]336[/tex]

and, senior ticket = [tex]15[/tex] and child ticket = [tex]11[/tex] of $[tex]312[/tex]

We need to find the price of ticket x and y

From Given data: [tex]12x+16y=336[/tex] and [tex]15x+11y=312[/tex]

= [tex]12x+16y=336[/tex]

= [tex]15x+11y= 312[/tex]

Multiply first equation with [tex]11[/tex] and second equation with [tex]16[/tex] we get

= [tex]132x+176y= 3696[/tex]

= [tex]240x+176y=4992[/tex]

by solving we get

= [tex]108x = 1296[/tex]

[tex]x=12[/tex]

putting the value of x in equation [tex]1[/tex] we get

= [tex]12\cdot12+16y=336[/tex]

= [tex]144+16y=336[/tex]

= [tex]16y=336-144[/tex]

= [tex]16y=192[/tex]

= [tex]y=12[/tex]

So, the value of senior ticket as well as child ticket is [tex]12[/tex]

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