SOLUTION: 40 adults and 26 went to see a movie on the opening screening and the revenue for the showing was $486.70. The next showing 20 adults and 31 kids went to see the same movie and the

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Question 1015122: 40 adults and 26 went to see a movie on the opening screening and the revenue for the showing was $486.70. The next showing 20 adults and 31 kids went to see the same movie and the revenue $332.45. How much was an adult ticket and how much was a kid ticket?

Answer by ankor@dixie-net.com(22740) (Show Source):
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40 adults and 26 kids went to see a movie on the opening screening and the revenue for the showing was $486.70.
The next showing 20 adults and 31 kids went to see the same movie and the revenue $332.45.
How much was an adult ticket and how much was a kid ticket?
:
let a = amt of adult ticket
let k = amt for kids
:
Write an equation for each showing
40a + 26k = 486.70
20a + 31k = 332.45
Use elimination here. Multiply the 2nd equation by 2, subtract the 1st equation
40a + 62k = 664.90
40a + 26k = 486.70
----------------------Subtraction eliminates a, find k
0 + 36k = 178.20
k = 178.20/36
k = $4.95 for kids
:
Use equation 20a + 31k = 332.45 to find a
20a + 31(4.95) = 332.45
20a + 153.45 = 332.45
20a = 332.45 - 153.45
20a = 179
a = 179/20
a = $8.95 for adults
:
:
Check these solutions in the 1st equation: 40a + 26k = 486.70
replace a & k
40(8.95) + 26(4.95) = 486.70
358.00 + 128.70 = 486.70