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

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

**ANSWER**:

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

**e** to represent the number of balloons

*Ethan*
began with and

**t** to represent the number of balloons

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

**e** = 3 ×

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

**e** - 10 = 2 ×
(

**t** + 10). Isolating for

**e**, we get:

**e** = 2 ×
(

**t** + 10) + 10. Since

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

**t** = 2 ×
(

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

**t** = 30. Theo began with 30 balloons and
Ethan began with 90. After giving Theo 10 balloons, Ethan had 80 balloons and Theo had 40 balloons. Ethan
needs to give Theo 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.)?