If you combine math with imagination, you get problem-solving ability. The exercise du jour (goodness...have I spoken French?....no, I've written it), requires a bit of imagination and a bit of math. The type of thinking involved is very practical and worth cultivating.
Given: You have the bottles. One of them is a 2-gallon bottle filled with a 40% solution of hxdroxyidiotic acid (I have invented this substance); one is a 2-gallon bottle filled with water; one is a 4-gallon bottle, which is empty. You have access to additional water at a nearby pump.
1. How would you create 4 gallons of a 20% solution of hydroxyidiotic acid?
2. How would you create 2 gallons of a 20% solution of hydroxyidiotic acid?
3. How would you create 1 gallon of a 20% solution of hydroxyidiotic acid?
4. How would you create 2 gallons of a 10% solution of hydroxyidiotic acid?
5. How would you create 1 gallon of a 10% solution of hydroxyidiotic acid?
Solution (no pun intended in light of the foregoing) to the last exercise:
If a person takes one step back for every two steps forward, it means that he or she only advances one step ahead for each two steps taken. This is actually a formula. If he or she were to take 20 steps in total, he or she would only have gained ten steps (i.e., be ten steps ahead) after having taken a total of 2o steps.