This is the continuation of the previous post on solving number problems. In this post, I will give three more examples on how to solve word problems about numbers.

**PROBLEM 4**

One number is smaller than the other by . Their sum is . What is the smaller number?

**Solution**

In the previous post, we talked about two numbers, one is being larger than the other. In this problem, the other number is smaller. If a number is , and the other number is smaller than it, then that number is . So, in the problem above, if we let be the number, then is the smaller number. Again, their sum is , so we can now set up the equation

Simplifying, we have . This gives us which means that . The smaller number is .

**Checking the Answer**

Is twelve less than ? Is their sum equal to ? If the answer to both questions is yes, then we are correct.

**PROBLEM 5**

Divide 71 into two parts such that one part exceeds the other by 8. What are the two numbers?

**Solution 1**

Let $let n$ be the smaller and be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation

larger number – smaller number =

which is equivalent to

Simplifying, we have . This gives us which implies that the larger number is . The smaller is .

**Solution 2**

Same as the solution of Problem 1. I leave this to you as an excercise.

**Checking the Answer**

Do the two numbers add up to . Does the number exceeds the smaller number by ?

**PROBLEM 6**

The sum of three consecutive even numbers is 90. What are the three numbers?

**Solution**

In the previous post, we talked about consecutive numbers. We know that consecutive numbers are numbers in uninterrupted succession. For instance, and are three consecutive numbers. In effect, if is the smaller number, the next two numbers are and . However, consecutive even numbers increases by such as , and . In effect, if is the smallest number, then is the middle number and is the largest number. Knowing their sum, we can now set up the equation

Simplifying, we have . This gives us and . So the consecutive even numbers are , and .

**Checking the Answer**

Are the three numbers even and consecutive? Is their sum equal to ? If the answers to both question is yes, then we are correct.

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