SOLUTION: hi math is not my best skill and i have tried and tried to get the correct answer for my homework, i was just wondering how to solve this problem: A local movie theater charges $12

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Question 708630: hi math is not my best skill and i have tried and tried to get the correct answer for my homework, i was just wondering how to solve this problem: A local movie theater charges $12 for an adult ticket and $10 for a child’s ticket. A group of eight people spent a total of $86 on tickets to a movie. How many adults and how many children were in the group? with the elimination method.. thank you very much.
Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A local movie theater charges $12 for an adult ticket and $10 for a child’s ticket. A group of eight people spent a total of $86 on tickets to a movie. How many adults and how many children were in the group?
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Quantity Equation: a + c = 8 persons
Value Equation:: 12a+10c = 86
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Modify:
a + c = 8
6a + 5c = 43
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Modify for elimination:
6a + 6c = 6*8
6a + 5c = 43
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Subtract to solve for "c":
c = 5 (# of child tickets)
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Solve for "a":
a + c = 8
a + 5 = 8
a = 3 (# of adult tickets)
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Cheers,
Stan H.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let an adult ticket be x and a child’s ticket y
A local movie theater charges $12 for an adult ticket and
$10 for a child’s ticket.
A group of eight people (adult and children)
x%2By=8................eq.1
spent a total of $86
12x%2B10y=86........eq.2
on tickets to a movie.
How many adults and how many children were in the group?
solve the system:
x%2By=8................eq.1....both sides multiply by 10
12x%2B10y=86........eq.2
_________________________with the elimination method

10x%2B10y=80................eq.1
-
12x%2B10y=86........eq.2.subtract eq.2 from eq.1
_________________________
10x%2B10y-12x-10y=80-86
10x%2Bcross%2810y%29-12x-cross%2810y%29=-6
-2x=-6....both sides multiply by -1
2x=6
x=6%2F2
highlight%28x=3%29.....# of adults in the group
now go back to eq. 1 and find y
3%2By=8................eq.1
y=8-3
highlight%28y=5%29......# of children in the group