Bessy and Bob algebra word problem

Bessy has 6 times as much money as Bob. But when each earns $6, Bessy will have 3 times as much money as Bob. How much does each have before and after earning the $6?


Let x be Bob's money, then Bessy's money is 6x

When Bob earns 6 dollars, his money becomes x + 6

When Bessy earns 6 dollars his money becomes 6x + 6

Now Bessy has 3 times as much money as Bob

so the equation is

6x + 6 = 3 * (x + 6)

6x + 6 = 3x + 18

6x + 6 - 6 = 3x + 18 - 6

6x = 3x + 12

6x - 3x = 3x - 3x + 12

3x = 12

x = 4

Before Bob and Bessy earned 6 dollars, Bob had 4 dollars and Bessy has 6 x 4 = 24

After they both earned 6 dollars, Bob had 10 dollars and and Bessy had 30 dollars.

Indeed 30 is 3 times 10.

Comments for Bessy and Bob algebra word problem

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Aug 21, 2017
This is a very good Question. NEW
by: Mathiscool

Thanks for this wonderful question and its solution,it helps me think of more ways to solve algebra.This site it great, keep up the good work.

Aug 14, 2017
Brilliant NEW
by: Kaycontinental

That is the first time I have ever seen a problem worked out like that, and I thought it was great. Only first, could you have suggested (I read this somewhere else) that you have to deduct (or add) to both sides?

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