Solving Word Problems in Numbers using Algebra Part 3

This is the last part of the Solving Number Problems Series. In this post, we are going to solve number problems in disguise, or numbers problems with different contexts. The previous two parts in this series you may want to read are Solving Word Problems in Numbers using Algebra are Part 1 and Part 2.

Example 7

Jack is twice as old as Rose. Two years from now, the sum of their ages is 40. How old are they now?

Solution

This problem is an age problem but it is very similar to number problems.  As stated, there are two points in time: now and 2 years from now.

Now, Jack is twice as old as Rose. That means that if Rose is 15, then Jack is 30. That means that if the age of Jack is 2x, then Rose’s age is x. Therefore, we have the following representation.  » Read more

Solving Number Problems Using Model Method

This is the second part of the Word Problem Solving Series on Numbers. In the previous post, I have shown you ways on how to solve number problems mentally by working backward. In this post, I am going to teach you how to use models, rectangles in particular, to solve the problems in the previous post. This representation is called the model method. The model method is very popular in Singapore.

Example  1

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

Let us represent numbers using rectangles. The first rectangle is the smaller number, and the second rectangle is the larger which is 1 more than the smaller. Clearly, if take away 1 from the larger number, the two numbers will be equal.

model method number problem

In addition, if we take away 1 from the larger number, then, we also have to take away 1 from the sum which gives us 46 after subtraction. Since the two rectangles have the same size, they will have to split 46 equally. This gives each large rectangle 23 each. This means that the smaller number is 23 and the larger number is 23 + 1 = 24. » Read more

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

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