Question 157845
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 doe each have before and after earning the $6?

If Bessy has 6 times as much as Bob, we can say the following:

Let 6x = Bessy's amount BEFORE she earn $6.

Let x = Bob's amount BEFORE he earns $6.

When Bessy earns $6, her new amount will be 6x + 6.

When Bob earns $6, his new amount will be x + 6.

After the increase of $6, Bessy "...will have 3 times as much money as Bob."

We write this as 3(x + 6).  The quantity (x + 6), if you go back and read my notes, represents Bob's new amount after he earns $6. The 3 infront of the parentheses will be multiplied as stated in the question.

We can now form our equation and it looks like this:

6x + 6 = 3(x + 6)....Solve for x.

6x + 6 = 3x + 18

6x - 3x = 18 - 6

3x = 12

x = 12/3

x = 4

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Is 4 the answer?  No, it is not.  We now use the value of x = 4 to find the before and after amounts for each person.

Bessy Before:

6x = 6(4) = $24

Bessy After:

6x + 6 = 6(4) + 6 = $30

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Bob Before:

x = $4....The value we found for x in our equation above.

Bob After:

x + 6 = 4 + 6 = $10

Did you follow?