Three adults and four children must pay 100. Two adults and three children must pay 70.

Question

Systems of Linear Equations and Problem Solving

Answer 1

Let a = adult price

Let c= child price

 

1).  3a + 4c = 100

2).  2a + 3c = 70

 

multiply equation 1 by 2

and multiply equation 2 by -3

 

6a + 8c = 200.   2(equation 1)

-6a -9c = -210.   -3(equation 2)

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add the two equations to eliminate a

 

-c = -10

c = 10

 

now we have c, plug into one of

the original equations to find a

 

3a + 4(10) = 100

3a + 40 = 100

3a = 60

a=20

 

adult tickets are $20

child tickets are $10