Question

Katherine is selling tickets to a soccer game. On the first day of ticket sales she...

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?

Math   Algebra   
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Answer #1

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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