ANgela R.

asked • 09/09/18

math word problems

Bessy has 6 times as much money as Bob, but when each earns $6, Bessy will have 4 times as much money as Bob. How much does each have before and after earning the $6?

Susan N.

If Bessy has 6 times as much money as Bob, we can say the following
Let x = Bob's amount before earning $6
then 6x = Bessy's amount before earning $6
When Bessy receives $6 her new amount will be 6x + 6
When Bob receives $6 her new amount will be x + 6
After the increase of $6, Bessy will have 4 times as much money as Bob
We can now form a new equation and it looks like this
6x + 6 = 3(x + 6)....Solve for x.
6x + 6 = 3x + 18
6x - 3x = 18 - 6
3x = 12

Solve for x
x = 12/3
x = 4
We now use the value of x to find the before and after of each person. 
Bessy Before:
6x = 6(4) = $24
Bessy After:
6x + 6 = 6(4) + 6 = $30
Bob Before:
x = $4....The value we found for x in our equation above.
Bob After:
x + 6 = 4 + 6 = $10
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09/09/18

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