Adult tickets cost $6.00 and children's tickets cost $4.00. 6 more children's over adult The total money he collects is $184. How many of each were sold?

Question

Miguel is selling tickets to a barbecue. Adult tickets cost $6.00 and children's tickets cost $4.00. He sells six more children's tickets than adult tickets The total amount of money he collects is $184. How many adult tickets and how many children's tickets did he sell?

 

 

From what I understand, this is a problem that requires you to set up an equation using variables to find a missing value. 

Answer 1

Hello, Jason

 

Lets start by identifying the variables and setting up the equations.

 

Let a represent the number of adult tickets

Let c represent the number of children's tickets.

 

6a  means that each adult ticket costs $6

4c  means that each children's ticket costs $4

 

1) 6a+ 4c  =  184

2) c= a+ 6

 

Equation #1 represents the total amount of money Miguel collected. And equation #2 says that 6 more children's tickets were sold than adult ticket.  

 

Now, I am going to substitute equation # 2 into equation #1.  

 

6a +  4c  = 184

6a+ 4(a+6)= 184          Do the distributive property

6a+4a+24  = 184

10a    + 24  = 184         Combining like terms

           -24      -24

             10a= 160         Dividing by 10

                  a= 16

So, there were 16 adult tickets sold.  And using equation # 2, c=a+6, we can determine that 22 children's tickets were sold.  You should check the answer by plugging 16 for a and 22 for c into equation # 1.

 

I hope this helps you out and thanks for posting.

 

D.Y. Taylor

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