   SEARCH HOME Math Central Quandaries & Queries  Question from Johan, a student: Two numbers whose difference is 16 and whose sum is 120 Hi Johan,

I think you are expected to use algebra to solve this problem. If so here are two approaches.

• Suppose the two numbers are $x$ and $y$ then you know that $x - y = 16$ and $x + y = 120.$ Solve these equations, perhaps by solving the first for $x$ and then substituting into the second.

• Suppose the smaller of the two number is $z$ the the larger must be 16 more, that is $z + 16.$ The sum of the two numbers is 120. Solve for $z.$

I however wouldn't use algebra to solve this. I instead would ask "Find two numbers whose difference is zero and whose sum is 120." That is I want the two numbers to be the same and their sum is 120. What are they? Increase one of the numbers by 1 and decrease the other by 1. Their sum is still 120 but their difference is 2. Increase the large by 1 and decrease the smaller by 1. Their sum is still 120. What is their difference? How many times do you have to do this until their difference is 16?

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.