can you provide alternative answer. don't understand the one provided.

charles had $120 more than benedict. charles gave 60% of his money to benedict. benedict then gave 25% to charles. in the end benedict had $20 more than charles. how much did charles have at first?

Hi Shirley,

Let me try to explain the solution first as this is a "More Than" style question which is typically solved with the model drawing approach.

A few notes:

• There are two transfers of money. In the first stage Charles transfers to Benedict (Steps 2 and 3). After Benedict transfers back another amount to Charles (Steps 4 and 5). We solve this is two stages with each stage managing the two independent transfers.


• When we deal with percentages, it is normally easier to work in fractions. So we convert the 60% and 25% to 3/5 and 1/4 respectively allowing us to divide the model up into units or parts.


• I use the red and green circles to show the transfer of units and money between the two individuals (Charles and Benedict).


• When transferring 60% (3/5) of Charles money, we must divide both the units and the money ($120) up as we are transferring 60% of everything that Charles has not just 60% of the units. Therefore, 3units and $72 are transferred (3/5 of 5 units --> 3 units, 3/5 of $120 is $72).


• Similarly when transferring from Benedict to Charles i.e. we take 25% (1/4) of everything that Benedict has which includes Benedit's original amount plus the additional money he just received from Charles.

got it! got confused with more than/less than model! thanks!

Chris Rogers wrote:
Hi Shirley,

Let me try to explain the solution first as this is a "More Than" style question which is typically solved with the model drawing approach.

A few notes:

• There are two transfers of money. In the first stage Charles transfers to Benedict (Steps 2 and 3). After Benedict transfers back another amount to Charles (Steps 4 and 5). We solve this is two stages with each stage managing the two independent transfers.


• When we deal with percentages, it is normally easier to work in fractions. So we convert the 60% and 25% to 3/5 and 1/4 respectively allowing us to divide the model up into units or parts.


• I use the red and green circles to show the transfer of units and money between the two individuals (Charles and Benedict).


• When transferring 60% (3/5) of Charles money, we must divide both the units and the money ($120) up as we are transferring 60% of everything that Charles has not just 60% of the units. Therefore, 3units and $72 are transferred (3/5 of 5 units --> 3 units, 3/5 of $120 is $72).


• Similarly when transferring from Benedict to Charles i.e. we take 25% (1/4) of everything that Benedict has which includes Benedit's original amount plus the additional money he just received from Charles.

I still don't understand the solution.

My confusion here is,

'On what basis is Charles and Benedict divided into five units which in the solution excluded the $120. Even if it is based on assumption, to apply 3/5 to $120 is beyond my comprehension.'

regards
Daniel

Hi Daniel

Let me try to explain this further for you.

At first Charles has $120 more than Benedict and then he, Charles, transfers 3/5 (60%) to Benedict. Before I continue let me take a slight comparison ....

Taking 60% of a total number, say 25, is the same as taken 60% of two numbers that when added together make 25, say 10 & 15. Using apples -->

If you had 25 apples (10 apples in box A and 15 apples in box and sold 60% (3/5) of the apples. Then you would have sold 3/5 of 10 apples from Box A --> 6 apples and 3/5 of 15 apples from box B --> 9 apples. You sold a total of 15 apples (3/5 of 25 --> 15).

Continuing ....
Like the apple example above, when Charles transfers 3/5 of his total money to Benedict we must transfer 3/5 of the $120 (he had $120 more) and 3/5 of the amount we do not know (represented by the bar). So we do not really exclude the $120 we just perform the 3/5 transfer in 2 steps since Charles' money consists of a known amount and an unknown amount. This should address your concern over why we take 3/5 of the $120.

For the second part of the question, Why do we break both Charles' and Benedicts "bar" into 5 units?
- Since we are trying to take 3/5 of Charles' money we must break Charles' bar into 5units. Then he transfers 3units to Benedict and keeps 2units for himself.
- Do you remember that the bar for Charles (excluding the $120) is the same as the bar for Benedict? Therefore, since we break Charles' bar into 5 units we do the same for Benedict (most important rule for model drawing --- Equal Parts).


I hope this addresses your questions. Let me know if you require further explaination.