   SEARCH HOME Math Central Quandaries & Queries  Question from Teresa, a parent: Hi, My 10yo son came home with this two problems and we can't figure out how to solve them. 1. Find two numbers whose sum is 43 and whose difference is 9 and 2. Find two numbers whose sum is 25 and whose difference is 11.. Many thanks Teresa Teresa,

At this level, use trial and error. An easy way is to check pairs that have the required difference. You will be assuming the answers to be whole numbers.

So for (1) check 1 and 10, 2 and 11,...

In a few years your son will learn how to solve problems like these using linear algebra; then he will not need to assume whole number answers any more.

Good Hunting!
RD

Teresa,

RD starts with numbers that have a difference of 9; 1 and 10, 2 and 11 and so on, looking for a pair with the sum of 43. Another approach is to start with numbers that have a sum of 43 and look for a pair with a difference of 9.

Half of 43 is 21 1/2 which is not a whole number but is half way between 21 and 22, and 21 + 22 = 43. Thus my first guess is 21 and 22. But their difference is only 1 so try 20 and 23, then 19 and 24 and so on.

I like these problems at your son's level. Practice with the trial and error (some teachers call it guess and check) will help you son gain some number sense.

Harley

Hi Teresa.

Sum: Let's say you start with one number and add a second number to it. You go "up" by that much.
Difference: When you start with the same first number and subtract the second number from it, you go "down" by the same amount.

This means that the original number must be exactly in the middle of the sum and the difference !

That's also called the average of the two numbers? Do you know how to find the average? Add the two numbers together, then divide in half.

Once you know the "middle" number, you can just reduce it by the difference amount to find the other number.

For example, you asked "Find two numbers whose sum is 43 and whose difference is 9." Well, I know one number is the average of these. So I can add 43 + 9 = 52 and then divide in half: 52 / 2 = 26. So one number is 26. The difference between the numbers is 9, so that means I can go up or go down by 9. Which one works?

Hope this helps,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.