Ratios

[jferguson]

Here is the problem:

The ratio of Julio's money to Marcus's money was 7:10. After Julio bought 4 books at $4.50 each the ratio of Julio's money to Marcus's money was 1:4. Use a bar graph to find how much money Julioo and Marcus have left.


Here is what I come up with: (each "-" represents a block)

Julio - - - - - - -
Marcus - - - - - - - - - -

[ $18.00]
Julio - - - - - - -
Marcus - - - -[-------]

The 6 blocks of Julios represents the $18.00 spent on books; each block = $3.00
Since Julio only has one block he has $3.00 and Marcus has 4 blocks, so he has $12.00. Total amount together would be $15.00.

I do not think this is correct because the begining ratio was 7/10 with Marcus having more money than Julio. Julio spent $18.00, so Marcus should have more than $12.00 since he did not spend any money. PLEASE HELP!!
Thank You

 

[mmm4444bot]

Blocks in ratio 7 to 10 are not the same size as blocks in ratio 1 to 4.

I mean, if you somehow come up with a value of $3 for the blocks in ratio 1 to 4, you need to convert to the smaller blocks, in order to assign any value to them.

I'm not sure that I remember how to solve these types of problems with bar-graph blocks of varying sizes.

I think that you need to find a connection between the relative sizes of blocks in different ratio.

Since the ratio of the block numbers for Marcus before and after is 10:4, the connection is that 2.5 small blocks (the ones in ratio 7:10) equal one large block (the ones in ratio 1:4).

10/4 = 5/2 = 2.5

Well, if 2.5 small blocks equal 1 large block, then there's 4.5 small blocks left over to equal $18, yes?

7 - 2.5 = 4.5

In other words, the $18 is divided by 4.5, to get $4 per small block.

Marcus has ten small blocks, so that's ten times $4.

Marcus did not spend any money, so the ending amount for Marcus is $40.

Julio started with 7 small blocks and then spent 4.5 of them, so that's $28 minus $18.

The ending amount for Julio is $10.

So, we see that blocks in ratio 7 to 10 are $4 each, while blocks in ratio 1 to 4 are $10 each.

Again, the conversion from small blocks to big blocks is 2.5

2.5 times $4 is $10.

I can draw a picture to help explain my thought process, if you like.

In the meantime, here's a different bar-graph, in case you need an extra one.

(Double-click image to expand, if needed.)

[attachment=0:3hxk6617]Chickeniness.JPG[/attachment:3hxk6617]