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The school that Kristen goes to is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 8 senior citizen tickets and 7 student tickets for a total of $146. The school took in $80 on the second day by selling 4 senior citizen tickets and 4 student tickets. What is the price each of one senior citizen ticket and one student ticket?
Solution
x = price of senior ticket
y = price of student ticket
create two equations representing amount of sales for tickets on two days
8x + 7y = 146
4x + 4y = 80
multiply second equation by 2 and subtract from 1st equation:
8x + 7y = 146
-(8x + 8y = 160)
-y = -14
y = 14
substitute 14 for y in 2nd equation and solve for x:
4x + 4(14) = 80
4x = 24
x = 6
$6 for senior tickets
$14 for student tickets