Math CentralQuandaries & Queries


Question from Elisabeth, a student:

Find two numbers with a sum of -8 and a difference of 4. Let x be the greater number and y be the lesser number.

Hi Elisabeth,

You can certainly solve the problem with the two variables $x$ and $y.$ You then have two equations. Since the sum is -8 you know that $x + y = -8.$ The difference is 4 so write this as an equation also and solve the resulting two equations for $x$ and $y.$

I would however prefer to approach the problem this way. Let $x$ be the greater of the two numbers. Since their difference is 4 you know the second number is 4 less than $x$ so it is $x - 4.$ The sum of the two numbers is -8 so $x + x - 4 = -8.$ solve for $x.$


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