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The Guess and Check Method is used when the information given is insufficient to solve in other methods. This method can also be used to solve questions that usually require Algebra.
Let's look at a few examples.
At first, the ratio of Shanti's savings to Roy's savings was 5 : 4. After each of them donated $60 to charity, the ratio of Shanti's savings to Roy's savings became 13 : 10. How much was Shanti's savings at first?
There are 2 sets of ratios in this question. We need to understand how the 2 sets of ratios relate to each other.
Let's organize the given information:
Now we'll draw models to help us understand the question.
Before: the ratio is 5 : 4 so we draw 5 boxes and 4 boxes. The boxes must be of equal size.
After: The ratio is 13 : 10 so we draw 13 boxes and 10 boxes. Again the boxes must be of equal size.
However, when we compare the 'before' and 'after' we must note that the final lengths of the 'after' ratios must be shorter than the original lengths of the 'before' ratios because they donated some money.
From the model we can see that the individual boxes (units) in the 'before' and 'after' ratios are of different sizes. We need to get them to be the same size. We do this by changing the ratio in the 'before' to equivalent units. (Multiply the 5 and the 4 by 2, 3, 4, 5.)
This method is called 'Guess and Check' because we have to use trial and error.
Now we need to figure out which of these numbers are closest to the 'after' ratio of 13:10.
Let's try 15 : 12
We need to take away some units from 15:12 to make it into 13:10. The units that we remove will represent the money donated to charity. Since they both donated the same amount of money, we must remove the same number of units from the ratio.
You can try this with the other ratios but you will not be able to get the final ratio of 13:10.
This is what it all means:
Before: Shanti has 15 units and Roy has 12 units. They each gave away 2 units. Shanti now has 13 units and Roy has 10 units.
So this tells us that 2 units represent $60 because they each donated $60.
2 units = $60
1 unit = $60 / 2 = $30
Shanti has 15 units at first, so 15 units = 15 x $30 = $450
Shanti's savings was $450 at first.