Model Method - Questions and Answers

Question posted by Beulah from country unknown:

Sum of two numbers is 2500. If 4% of one number is 6% of the other, find the numbers.


Step 1: Draw a long bar to represent one of the two numbers. Divide the bar into 2 parts since this number is made up of two parts: 6% and 94%.

However, since 6% of this number is equal to 4% of the other number, the percentages have different values in the two numbers separately, i.e., 1% of the first number is not equal to 1% of the second number.

To facilitate comparison, we will need to convert the percentages for both number into a comparable unit of measurement. In this question, we will convert all the percentages into units.

For the first number, we will convert 100% into 100 units. So, we will label the shorter part as 6 units and the longer part as 94 units.


Step 2: To make the second number comparable to the first, we need to convert its percentage into units as well.

Since it was given in the question that 6% of the first number is equal to 4% of the second number. 4% of the second number must be equal to 6 units.

So, we draw a box identical to the 6 units of the first number and label it 6 units (this 6 units is equivalent to 4% of the second number).


Step 3: Using the 3-lined Method, we can easily find out how many units is 96% of the second number equal to.

4% ----------> 6 units

1% ----------> 6/4 units

96% --------> 6/4 X 96 = 144 units

We then draw a longer box to its right to represent the remaining 96% of the second number (which is equivalent to 144 units as found from the workings above).

We also add in a bracket to the extreme right of the model to show the total of the 2 numbers is 2500.


From the model, we can see that,

Since first number = 6 units + 94 units = 100 units

And second number = 6 units + 144 units = 150 units

First number + second number = 2500

100 units + 150 units ----------> 2500

250 units ----------> 2500

1 unit ----------> 2500/250 = 10

100 units ----------> 100 X 10 = 1000

150 units ----------> 150 X 10 = 1500

Therefore the 2 numbers are 1000 and 1500.

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