SOLUTION: 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 ma

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Question 825199: 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?

a. Write a system of linear equations based on the description. Use x to represent the
number of adults and y to represent the number of children.
b. Solve the system using the elimination method. Show all the steps leading to your
answer.
c. Write 1-2 sentences to explain what the solution means for this situation.
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
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x = number of adult tickets purchased
y = number of child tickets purchased
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x + y = 8
12x + 10y = 86
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copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution by matrix method:
x = number of adult tickets purchased = 3
y = number of child tickets purchased = 5
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system matrix
1 1
12 10
---
inverse of system matrix
-5 0.5
6 -0.5
---
determinant of system matrix = -2
---
now solve by elimination:
---
(x + y = 8)(-10)
12x + 10y = 86
---
-10x - 10y = -80
12x + 10y = 86
---
add the system:
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2x = 6
---
x = 3
---
x + y = 8
3 + y = 8
---
y = 5
---
solution by elimination method:
x = number of adult tickets purchased = 3
y = number of child tickets purchased = 5
---
NOTE:
solution by matrix method agrees with solution by elimination method
---
the solution means that 3 adult tickets and 5 child tickets were purchased.
---
Solve and graph linear equations:
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---
Solve quadratic equations, quadratic formula:
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Solve systems of linear equations up to 6-equations 6-variables:
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