Math CentralQuandaries & Queries


Question from belinda, a parent:

The product of two numbers is 2400, one number is 20 more than the other number. what are the two numbers?


This is a candidate for what is sometimes called "guess and check". This technique involves making an intelligent guess (I would rather use the term estimate) and then modifying your estimate to find the correct answer. In this problem the "intelligent" part of the guess is to think of the number that is half way between the two numbers you want. Just so that I can talk about this number I am going to call it x. Thus the numbers you want are 10 more than x and 10 less than x. Since the product of the two numbers is 2400 the product of x with x should be approximately 2400, that is x2 is approximately 2400. But 2400 is close to 2500 and 502 = 2500 so x should be close to 50.

Can you complete it now?


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