A matinee ticket costs $6 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who saw a movie was 35, and the total money collected was $70. Which of the following options represents the number of children and the number of adults who saw a movie that day, and the pair of equations that can be solved to find the numbers?
7 children and 28 adults
Equation 1: a + c = 35
Equation 2: 6a − c = 70
7 children and 28 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70
28 children and 7 adults
Equation 1: a + c = 35
Equation 2: 6a + c = 70

- automaticloveletter

- jamiebookeater

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- anonymous

Just a heads up. On your other question about the elimination method, the first person to answer your question was wrong. I showed you how to do the problem and my answer checked out. You may want to visit it.

- anonymous

I can work with you on this problem now.

- automaticloveletter

Please c:

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## More answers

- anonymous

Okay let's break it down. Let's start with the first information given to us: $6 per adult and $1 per child. We don't know what the numbers of adults and children are so we need to assign each a variable. Let "a" stand for number of adults and "c" for number of children.

- anonymous

Does that make sense?

- automaticloveletter

Yes

- anonymous

So basically the sentence "$6 per adult" is equal to the expression: 6a. and "$1 per child" is equal to the expression 1c.

- anonymous

If we took those two expressions and added them together, would you agree that we would find the total cost of this trip to the movies?

- automaticloveletter

Yeah

- anonymous

Okay. lets say the total cost is represented by an x. The equation would be 6a+1c=x.

- automaticloveletter

Yeah, I get that part

- anonymous

We can fill in the x variable because in the problem it says that the total money collected was $70. So now the equation would be: 6a+1c=70.

- automaticloveletter

I know

- anonymous

we can drop the 1 in front of the c and the equation's value wouldn't change: 6a+c=70.

- anonymous

next you would take the number of adults and the number of children and add them together to find the total number of people that came.

- anonymous

Can you figure out that equation?

- automaticloveletter

No that's where I got stuck

- anonymous

Okay. Well, remember when I said that our variables would be "a" for the NUMBER OF ADULTS and "c" for the NUMBER OF CHILDREN? To find the total number of people who came, you would take the NUMBER OF ADULTS and the NUMBER OF CHILDREN and add them together to get the total number of people which according to the directions is 35.

- automaticloveletter

Ah okay

- anonymous

Your equation would simply be a+c=35.

- automaticloveletter

So it's either B or c

- anonymous

yes. now we just have to solve the equations. Do you want help with that?

- automaticloveletter

I'm leaning towards C

- anonymous

That's correct! Great job! :)

- automaticloveletter

Thank you for helping me c:

- anonymous

You're very welcome! I enjoyed it! :) :) :)

- anonymous

Did you check out my answer to your other question yet? You would multiply the bottom equation by -3.

- automaticloveletter

I did. Thanks again. :)

- anonymous

No problem! :)

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