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Sunday, August 20 2017 @ 09:51 PM CDT
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 ratio question- help
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By: Strawberry (offline)  Tuesday, February 19 2013 @ 10:42 AM CST (Read 605 times)  
Strawberry

The ratio of John's money to Daisy's money was 1: 8. When John spent $80 and Daisy spent $985, John had 3 times as much money as Daisy. How much money did John have at first?

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By: Terribleplayer (offline)  Tuesday, February 19 2013 @ 01:06 PM CST  
Terribleplayer

It can be solved using models but it is a hassle to explain it here and in my opinion takes longer than the method I'm going to show below:

John in end --> 3 units
Daisy in end --> 1 unit
John at first ---> 3 units + 80
Daisy at first --> 1 unit + 985

As John only has one-eighth of Daisy at first, we need to multiply John's amount by 8 to balance them and make both equal:

John at first x8 --> 24 units + 640
24 units + 640 --> 1 unit + 985
23 units --> 985 - 640 = 345
1 unit --> 15
John at first (3 x 15) + 80 = 125

This might seem a little algebraic but is actually just the concept of making both sides equal. Do note I'm working backwards.
Another approach that is similar but just as fast and useful is to work forwards:

John at first --> 1 unit
Daisy at first --> 8 units
John in end --> 1 unit - 80
Daisy in end --> 8 units - 985

Again we need to balance, but this time, it is daisy who needs to multiply by 3 as she only has one-third of John in the end:

Daisy in end x3 --> 24 units - 2955
24 units - 2955 --> 1 unit - 80
23 units --> -80 + 2955 = 2875
John at first (1 unit) --> 125

For this particular question, the first method of working backwards is more preferable because you don't have to deal with negative numbers.
If you want to know the model method, do ask. The numbers involved are similar, just the presentation is different.

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