How to Solve Number Word Problems Part 1

In the previous post, we have learned How to Solve Number Problems Mentally. In this post, we are going to solve the same word problems algebraically. The objective of this post is for you to be able to learn how to set up equations based on given problems. Once you know how to set up equations for easy problems, it will be easier for you to do so using harder problems which we will discuss in the latter parts of this series. Note that before solving these problems, it is already assumed that you know how to solve equations.

Problem 1

One number is 3 more than the other. Their sum is 45. What are the numbers?

Scratch Work

The strategy in solving algebraic problems is to take a specific case. For instance, in the problem above, if one number is say, 5, then the larger number is 5 + 3 because it is 3 greater than the first number. Since we do not know the numbers yet, we can represent the smaller number by x and the larger number by x + 3.

The next clue is the word “sum,” their sum is 45. So, sum means you have to add the two numbers which are x and x + 3. In sentence form, the sum of x and x + 3 is 45 or

x + (x + 3) = 45

in equation form. Now, we write the solution.

Solution

Let x be the smaller number and x + 3 be the larger number.

x + (x + 3) = 45

2x + 3 = 45

2x = 42

x = 21

So, the smaller number is 21 and the larger number is

x + 3 = 21 + 3 = 24.

Of course, after this, you can always do the checking by looking at the conditions. Is the larger number greater than 3? Is the sum of two numbers 45? Once the answer satisfies all the conditions in the given problem, then it is correct.

Problem 2

The sum of two numbers is 53. One number is 7 less than the other. What are the numbers?

Scratch Work

In this example, if the larger number is 100, then the other number is 7 less than the 100 or 100-7. So, if the number is x, the smaller number is x - 7. The next sentence is their sum is 53, so we have to add x and x -7 forming the equation

x + (x - 7) = 53.

We now write the solution.

Solution 

Let x be the larger number and x - 7 be the smaller number.

x + (x-7) = 53

2x - 7 = 53

2x = 60

x = 30

Therefore, the larger number is 30 and the smaller number is x - 7 = 30 - 7 = 23. Again, you can check the answer by if it satisfies the conditions above.

Problem 3

One number is twice the other number. Their sum is 45. What are the numbers?

Scratch Work

If one number is 5, then the number twice it is 10, or 2(5). Therefore, if one number is x, the number twice it is 2(x) or 2x. Next, their sum is 45. It means that if you add x and 2x, the sum is 45. Or, x + 2x = 45.

Solution

Let x be the smaller number and 2x be the larger number.

x + 2x = 45

3x = 45

Dividing both sides by 3, we have

x = 15.

Therefore, the smaller number is 15 and the larger number is 2(15) = 30. Checking it, 30 is indeed twice 15, and yes, their sum is 45.

Note: This post has a video version. In the video, these problems were solved in Taglish.

In the second part of this series, we will learn to solve more complicated number word problems.

Related Posts Plugin for WordPress, Blogger...

You may also like...

3 Responses

  1. May 2, 2014

    […] the option to watch some important posts in Ph Civil Service on video. Below are the videos of  How to Solve Number Word Problems Part 1 in Taglish. You can see the original problems in the preceding […]

  2. August 20, 2015

    […] (2) How to Solve Number Problems Part 1  […]

  3. August 20, 2015

    […] already had three problems in the first part of this series, so let’s solve the fourth […]

Leave a Reply

Your email address will not be published. Required fields are marked *