Name: Jason

Level: Middle

Question:

An older brother said to his younger brother, "Give me 8 of your CDs, then I will have twice as many as you." The younger brother replied, "No, you give me 8 of yours instead, and then we'll have an equal number." How many CDs does each boy have?

I have had no algebra (6th grade), and my teacher says that it can be done without equations. Please explain how this can be done.

Thank you very much!

Jason

Hi Jason,

Make four columns: the first two have the headings "young brother before" and "after", and the last two have the "old brother before" and "after". Then start with a guess, say the young brother starts with 20 CDs, and fill in the other three columns for the case

(a) when he gives 8 CDs away to his brother,
and for case

(b) when he gets 8 CDs from his brother.
Caseyoung brother beforeyoung brother after old brother beforeold brother after
a20
b20

Do the "before" columns agree? You see that it wasn't a good first guess. Must the young brother have more or fewer than 20? So use the bad first guess to make a better second guess.

Chris
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