IBefore teaching algebra, it might be a good idea to teach different types of problems that can be solved without algebra. It teaches mathematical manipulation and provides some interest to see how these same problems can be solved with algebra.

Here is another one. Since I have not had many visitors, I will also give the solution. You can try to find the solution before reading it.

The sum of two numbers is 20 and the difference between the two numbers is 6. What are the two numbers?

Solution:

Let’s start by looking at both numbers equal to 10. The sum is 20, but the difference is 0. If we add 1 to one of the tens and subtract 1 from the other, we still have the sum being 20, but now the difference is 2, since adding and subtracting 1 will each increase the difference by 1. It therefore follows that by adding a number to one 10 and subtracting the number from the other 10 will give a sum of 20 and a difference of twice the number. To get a difference of 6 we add and subtract 3, giving 10+3=13 and 10–3=7.