## Math Word Problems: Solving Number Problems Part 4

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 $x$ be the first number, $x + 1$ be the second number, and $x + 2$ be  third number.  As the problem says, the sum of the first two, $x +(x + 1)$ is $20$ more than the third. This means that if we add $20$ to the third number, $(x + 2) + 20$, it will be equal to the sum of the sum of the first two. We now set up the equation

$x + (x + 1) = (x + 2) + 20$.

Simplifying, we have $2x + 1 = x + 22$. This means that $x = 21$. So, the three consecutive numbers are $21$, $22$, and $23$. » Read more

## Math Word Problems: Solving Number Problems Part 3

This is the third part of the Solving Number Problems Series. The first part can be read here and the second part can be read here.  In this post I will continue worked examples using problems which are slightly more complicated than the problems in the previous two parts. Without further ado, lets start with the seventh problem in the series.

PROBLEM 7

Twice a number added to $18$ is $5$ times that number. What is the number?

Solution

In the two previous posts, we have learned that if $n$ is a number, then twice that number is $2n$. So, twice a number added to $5$ is represented by $2n + 5$. Now, that number, the $2n + 5$ is five times that number of $5n$. So, we can now set up the equation

$2n + 18 = 5n$.

If we solve for $n$, we have $n = 6$» Read more

## Math Word Problems: Solving Number Problems Part 2

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 $12$. Their sum is $102$. 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 $15$, and the other number is $6$ smaller than it, then that number is $15 - 6$. So, in the problem above, if we let $n$ be the number, then $n - 12$ is the smaller number.  Again, their sum is $102$, so we can now set up the equation » Read more