Systems of Linear Equations

Question

A group of adults and kids went to see a movie. Tickets cost 7$ each for adults and 2.50$ each for kids, and the group paid 39$ total. There were 8 fewer adults than kids in the group. How many adults and kids were in the group?

Answer 1

For me, this is a type of "trial and error" problem.

 

With the information given, you would first need to make an equation to represent the information, which would go as follows:

 

7x+2.5y=39 

 

As can be determined from the word problem, the "x" represents the adults and the "y" represents the kids, which together should equal $39.

 

Since there are 8 fewer adults than kids in the group, I would first start with 1 adult and 8 kids:

 

7(1)+2.5(8)=39

7+12.5=39

19.5=39 is not correct so I would then move on to 2 adults and 10 kids:

 

7(2)+2.5(10)=39

14+25=39

39=39, which is correct and therefore, it can be inferred that there were 2 adults and 10 children in the group.