Math CentralQuandaries & Queries


Question from Donna, a parent:

The sum of two numbers is 39.  The difference is 11.  What are the numbers?

Hi Donna.

When you have a sum and a difference and add them together, that is the same as doubling one of them.

For example, if the two numbers are 7 and 4, then the sum is 11 and the difference is 3. When we add the sum and the difference together, we get 14, which is double the original 7.

If you add your sum and difference together, then take half of the result, you have one of the numbers. From that, it is easy to find the other number because adding the second number to the first has to be 39.

If you are studying algebra, the following will make sense to you:

Let a and b be the two original numbers.

The sum is a+b.

The difference is a-b.

Adding the sum to the difference is (a+b) + (a-b) which is a + b + a - b = 2a. So you see that half of this is one of the original numbers (a).

Stephen La Rocque.

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