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

Question

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

anonymous · Answer

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 · Answer

I can work with you on this problem now.

automaticloveletter · Answer

Please c:

anonymous · Answer

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 · Answer

Does that make sense?

automaticloveletter · Answer

Yes

anonymous · Answer

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

anonymous · Answer

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 · Answer

Yeah

anonymous · Answer

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

automaticloveletter · Answer

Yeah, I get that part

anonymous · Answer

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 · Answer

I know

anonymous · Answer

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

anonymous · Answer

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 · Answer

Can you figure out that equation?

automaticloveletter · Answer

No that's where I got stuck

anonymous · Answer

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 · Answer

Ah okay

anonymous · Answer

Your equation would simply be a+c=35.

automaticloveletter · Answer

So it's either B or c

anonymous · Answer

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

automaticloveletter · Answer

I'm leaning towards C

anonymous · Answer

That's correct! Great job! :)

automaticloveletter · Answer

Thank you for helping me c:

anonymous · Answer

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

anonymous · Answer

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

automaticloveletter · Answer

I did. Thanks again. :)

anonymous · Answer

No problem! :)