On the first day of sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75. The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price each of one senior citizen tickets and one child tickets?

ANSWER:The price of senior citizen ticket is $4 and price of child ticket is $7. SOLUTION: Given, first day of sales the school sold 3 senior citizen tickets and 9 child tickets for a total of $75.  The school took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets.  We need to find what is the price each of one senior citizen tickets and one child tickets. Let, the price of senior citizen ticket be "x" and price of child ticket be "y" Then according to the given information, 3x + 9y = 75 x + 3y = 25  [by cancelling the common term 3. x = 25 – 3y ---- (1) And, 8x + 5y = 67 ---- (2) Substitute (1) in (2) 8(25 – 3y) + 5y = 67 200 – 24y + 5y = 67 5y – 24y = 67 – 200 -19y = -133 y = [tex]\frac{133}{19}[/tex]y = 7 Now substitute y value in (1) x = 25 – 3(7) x = 25 – 21  = 4 Hence, the price of senior citizen ticket is $4 and price of child ticket is $7.