Ethan and Leo are getting ready for a friendly water balloon fight when Leo protests *"Wait, it's
not fair, you have three times as many balloons as I do!"* Ethan, being a good sport, hands Leo ten
more balloons. *"It's still not fair"* Leo says, *"you still have twice as many balloons as I
do!"*

How many more balloons must Ethan give Leo so that each of them have the same number?

**ANSWER**:

*Ethan must give Leo 20 more balloons.*
**EXPLANATION**: Let's use

**E** to represent the number of balloons

*Ethan*
began with and

**L** to represent the number of balloons

*Leo* began with. Ethan had
three times as many balloons to begin, so

**E** = 3 ×

**L**. After Ethan
gave 10 balloons to Leo, he had twice as many ballons. So,

**E** - 10 = 2 ×
(

**L** + 10). Isolating for

**E**, we get:

**E** = 2 ×
(

**L** + 10) + 10. Since

**E** has been isolated in two equations, we know the
right hand side of the two equations are equal, therefore: 3 ×

**L** = 2 ×
(

**L** + 10) + 10 which works out to

**L** = 30. Leo began with 30 balloons and
Ethan began with 90. After giving Leo 10 balloons, Ethan had 80 balloons and Leo had 40 balloons. Ethan
needs to give Leo another 20 balloons so that they have have 60 balloons.

Do you have a

suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?