Business Math: Bessy has 6 times as much money as Bob, but w

[hayhay1084]

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 money does each have before and after earning the $6?

Please help!!! This does need to be solved in an algebraic form. This really isn't pre-algebra. sorry!

 

[stapel]

Since you have posted this exercise to "Pre-Algebra", I will assume that you need a non-algebraic method for solving this.

Draw pictures to represent each situation. Since the money is given in terms of multiples of Bob's amount, use the basic unit "box" to represent Bob's original amount. At first, Bessy has six times as much as Bob.

       |---|---|---|---|---|---|
Bessy: |   |   |   |   |   |   |
       |---|---|---|---|---|---|

       |---|
Bob:   |   |
       |---|

When each has six dollars more, Bessy has only three times as much as Bob. The "six dollars more" can be distributed in Bessy's diagram, and the total partitioned to indicate the "three times more" that she has:

       |---||---|| |---||---|| |---||---||
Bessy: |   ||   || |   ||   || |   ||   ||
       |---||---|| |---||---|| |---||---||

       |---| --- |
Bob:   |   | $6  |
       |---| --- |

This last diagram shows that one original unit, plus six, equals two original units, plus two. That means that one original unit plus two equals six. How much, then, is one original unit?

Eliz.

 

[Denis]

IF it is algebra, then:
Let money Bob has = x ; then Bessy has 6x

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