This is the fourth and last part of the Number Word Problem Solving Series, the first subtopic in the Word Problem Solving Series. In this post, I will post more word problems with solutions. We start with the tenth problem in the series.

**PROBLEM 10**

There are three consecutive numbers. The sum of the first two is 20 more than the third. What are the numbers?

**Solution**

Let be the first number, be the second number, and be third number. As the problem says, the sum of the first two, is more than the third. This means that if we add to the third number, , it will be equal to the sum of the sum of the first two. We now set up the equation

.

Simplifying, we have . This means that . So, the three consecutive numbers are , , and .

**Checking the Answer**

The sum of the first two integers . This is more than , the third number. So, we are correct.

**PROBLEM 11**

In a three digit number, the tens digit is half the hundreds digit. The ones digit is less than the tens digit. If the sum of the digits is , what is the number.

**Solution**

Let be hundreds digit. The tens digit is half of it, so it’s . Then, the ones digit is less than the tens digit or . Since the sum of the three digits is , we can set up the equation

.

Multiplying both sides by , we have

.

That gives us , and . Therefore, the tens digit is and the ones digits is . So, the number is .

**Checking the Answer**

The tens digit is half of the hundreds digit . The ones digit is , one less than the tens digit.

**PROBLEM 12**

The sum of two numbers is . Three times the smaller is less than the larger.

**Solution**

Let be the smaller number and be the larger number. Three times the smaller, is less than the larger. This means that if we add to , it will be equal to the larger number which is . So, we set up the equation

Simplifying, we have which means that . The other number is .

**Checking the Answer**

Left as an exercise.

***

In the next series, we will discuss word problems involving age. We will have 12 sample problems with solutions.

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