Math CentralQuandaries & Queries


Question from Feni:

The sum of two numbers is 4. The difference of the two numbers is 2. What are the two numbers?


I think the object of this problem is to have you set up two algebraic equations and then solve them but let's try something differen first. Think of two, non-negative integers which have a sum of 4. What is their difference? If it is 2 you have found the answer, if not try two different non-negative integers which have a sum of 4. In a couple of tries you should find the answer.

Now let's try the algebraic approach. Suppost the larget if the two numbers is $x$ and the smaller is $y.$ The sum of the two integers is 4 so $x + y = 4.$ $x$ is the larger and the difference is 2 so $x - y = 2.$ Can you solve these two equations? Did you get the same answer as you did without algebra?

I hope this helps.

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