Math CentralQuandaries & Queries


Question from a student:

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


I want to show you two ways to approach this problem, one using algebra and the other using number sense. I expect that your teacher expects the algebraic approach but I prefer the number sense method.

Algebraic method.

Suppose that the smaller of the two numbers is $s.$ The second number is 2 more then $s$ so the second number is $s + 2.$ The sum of the two numbers is 4. Write this as an equation and solve for $s.$ Make sure you verify your answer.

Number Sense method.

Suppose the question was "The difference of two numbers is 0, and their sum is 4. What are the numbers?" In this case the numbers are $2$ and $2.$ But you want the difference between the two numbers to be $2.$ If you increase one of the two's by one to get $3$ and decrease the other by one to get $1$ then their sum will still be $4$ but their difference will be $2.$

I hope this helps,

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