SOLUTION: A group of 60 people attend a ball game. There were twice as many children as adults in the group. Write a system of equations that you could use to set up this problem, where "a"

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A group of 60 people attend a ball game. There were twice as many children as adults in the group. Write a system of equations that you could use to set up this problem, where "a"       Log On


   

Question 581662: A group of 60 people attend a ball game. There were twice as many children as adults in the group. Write a system of equations that you could use to set up this problem, where "a" is the number of adults and "c" is the number of children in the group. Solve the system of equations for "c", the number of children in the group.
Show the work step by step and explain how you did it.
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Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A group of 60 people attend a ball game. There were twice as many children as adults in the group. Write a system of equations that you could use to set up this problem, where "a" is the number of adults and "c" is the number of children in the group. Solve the system of equations for "c", the number of children in the group.
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Equations:
a + c = 60
c = 2a
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Substitute for "c" and solve for "a":
a + 2a = 60
3a = 60
a = 20 (# of adults)
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Solve for "c":
c = 2a
c = 2*20 = 40 (# of children)
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cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = number of adults, and c = number of children


"A group of 60 people attend a ball game" means that a + c = 60.

"There were twice as many children as adults in the group" means that c = 2a

So the system of equations is
a + c = 60
c = 2a


Now let's solve for c

a + c = 60

a + 2a = 60

3a = 60

a = 60/3

a = 20

So there are 20 adults

c = 2a

c = 2(20)

c = 40

and there are 40 children


Note: add up the two counts to get 40+20 = 60, so this checks the first condition (that there are 60 people). Also, notice how 40 kids is exactly double 20 adults.