Most of us would always take a pen and solve for x if we see word problems. But did you know that you can solve them by working backward or even mentally? In this post, I am going to teach you some techniques on solving problems by working backward.

Example 1: One number is three more than the other. Their sum is 45. What are the numbers?

Solution

In the given, one number is 3 more than the other. This means that if you subtract 3 from the larger number they will be equal. Note that if we subtract 3 from one of the numbers, then we should also subtract 3 from their sum. Therefore, their sum will be 45 – 3 = 42. Since the numbers are equal, we now divide the sum by 2. That is, 42/2 = 21.

So, the smaller number is 21 and the larger is 21 + 3 = 24.

Check: 21 + 24 = 45

Example 2: One number is 5 less than the other. Their sum is 43. What is the smaller number?

Solution

This is very similar to Example 1. Here, one number is 5 less than the other; so, if we add 5 to the smaller number, they will be equal. If we add 5 to the smaller number, we should also add 5 to their sum. Therefore, their sum will be 43 + 5 = 48. Since the two numbers are equal, we can divide the sum by 2. That is 48/2 = 24. Since we added 5, it means that 24 is the larger number. So, the smaller number is 24 – 5 = 19.

Check: 19 + 24 = 43

In the next post, we are going to discuss more examples.