Katherine is selling tickets to a soccer game. On the first day of ticket sales she sold 3 senior citizen tickets and 9 child tickets for a total of $75. She made $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of one senior citizen ticket and one child ticket?
Let price of one senior citizen ticket and one child ticket be x and y respectively.
According to the question-
3x + 9y = 75 ......(I)
8x + 5y = 67 .....(II)
(I) 8 & (II) 3 IMPLIES
24x + 72y = 600 .....(III)
24x + 15y = 201 ......(IV)
(III) -(IV) implies
57y = 399 y = 39957 y=7
Putting this value in (I) we get -
3x + 63 = 75
3x = 75 - 63
3x = 12
x = 4
So, price of one senior citizen ticket is $4 and price one child ticket is $7.
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