Category: High School Algebra

Solving Math Word Problems in Numbers Using Algebra Part 2

High School Algebra, High School Mathematics

This is the fourth part of the Word Problem Solving on Number Problems and this is the continuation of the Solving Word Problems in Numbers in Algebra.  In this post, we discuss more examples on how to solve number problems. We start with the fourth example.

Example 4

The sum of three consecutive numbers is 78. What are the three numbers?

Solution

In the previous post in this series, we have already discussed how to solve problems about two consecutive odd integers. In this example, there are three consecutive integers, not odd and not even. As we can see, 11, 12, and 13 are consecutive integers and we only add 1 each time to get the next number. This means that if x is the smallest number, then x + 1 and x + 2 are the next two integers. » Read more

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Solving Math Word Problems in Numbers Using Algebra

High School Algebra, High School Mathematics, Problem Solving and Proofs

This is the third part of the Solving Math Word Problem Solving Series on Numbers for Grade 6 – 8 students. The first part was on solving number problems mentally by working backward. The second part discussed on solving number problems using the model method. In this post, we are going to discuss how to solve word problems using Algebra if the mental and model methods fail. We will start with simple problems and will continue to solve more complicated problems later. We will use the problems we discussed in the first two parts of this series. Note that the discussion in this post is quite detailed because it is designed for beginners particularly middle school and high school students.

Example 1 One number is 1 more than the other. Their sum is 47. What are the numbers?

Solution

First Sentence: One number is 1 more than the other.

If there are two numbers and the other one is 1 bigger than the number, then if the smaller number is 5, the other is 5 + 1 or 6. So, since we don’t know what the number is, we let the number n. This means that the larger number is n + 1.  » Read more

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Number Word Problems 1 – How to Solve Number Problems Mentally

High School Algebra, High School Mathematics, Problem Solving and Proofs

This is the first part of the Solving Number Problems Series for Grade 6-8 students, a-sub series of the Math Word Problem Solving Series.

Some of you probably need paper and pencil to solve number problems. You will be surprised that if you think harder and work backward, you can actually solve these problems in your head. Consider the following examples.

Example 1

One number is 1 more than the other. Their sum is 47. What are the numbers?

Explanation and Solution

First, one number is 1 more than the other. That means that if we subtract 1 from the larger number the two numbers will be equal. That’s our first clue.

Second, if we subtract 1 from the larger number, then we should also subtract 1 from the sum (Can you see why?). That makes the sum 46. Now, since the two numbers are equal, we can divide 46 by 2. That gives us 23 which is the smaller number. Now, since the other number is 1 larger than 23, then it is 24.

Answers: 23 and 24 » Read more

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