Write an solve the system of equations.

Question

A group of 84 people attend a movie. There were 5 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.

Answer 1

Here's the system of equations:

a + c =84 (the total number is adults and children)

5a = c (the number of children is five times the number of adults)

 

From here, it's a simple case of substitution due to having a value for c:

5a + a = 84

6a = 84

Divide both sides by 6:

a = 14

 

Now that we know the number of adults, we can find the children:

c = 5 * 14

c = 70

 

Check:

14 + 70 = 84

84 = 84