Maggie's brother is 4 years younger than four times her age. The sum of their ages is 31. How old is Maggie?

First, determine the terms.
For Maggie, let’s use the variable m.
For her brother, it is (4m-4).
Their ages together is 31.

Let’s combine to make an equation:
(4m-4)+m=31
First, combine like terms on the left
5m-4=31
To begin isolating m, add 4 to both sides
5m-4=31
+4 +4
—————-
5m=35
To completely isolate m, divide both sides by 5.
5m=35
—— —-
5 5
From here, you get
m=7

You can check by putting this into the original equation.
(4(7)-4)+7=31
(28-4)+7=31
24+7=31
31=31

Therefore, Maggie is 7 years old.