Question 873750: One adult ticket and five children's tickets cost $31. Two adult tickets and eight children's tickets cost $53. How much does one adult ticket cost? How much does one children's ticket cost?
Answer by LinnW(1048)   (Show Source):
You can put this solution on YOUR website! set a = price of adult ticket
c = price of child ticket
a + 5c = 31
2a + 8c = 53
Working with a + 5c = 31 , add -5c to each side, a = 31 - 5c
Substitute (31 - 5c) for a in 2a + 8c = 53
2(31 - 5c) + 8c = 53
62 -10c + 8c = 53
62 -2c = 53
add -62 to each side
-2c = -9
c = 9/2 = 4.5
Substitute 9/2 for c in a = 31 - 5c
a = 31 - 5(9/2)
a = 31 - 45/2
a = 62/2 - 45/2
a = 17/2 = 8.5
Let's check our equations
a + 5c =? 31 , 8.5 + 5*4.5 , 8.5 + 22.5 , 31
2a + 8c =? 53 , 2(8.5) + 8(4.5) , 17 + 36 , 53
Our equations check so adults are 8.50 and children are 4.50
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