Question 157845This question is from textbook Practical Business Math Procedures
: 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?
This question is from textbook Practical Business Math Procedures
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! 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?
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