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?
Solution
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.
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