How to Solve Consecutive Number Problems Part 3

This is the third part of the Solving Consecutive Number Problems Series. In this post, we solve more problems about consecutive numbers. We have already discussed four problems in the first part and second part of this series, so we start with the fifth example.

Example 5

There are 3 consecutive odd numbers. Twice the smallest number is one more than the largest. What are the numbers?

Solution

In the first post in this series, we have learned that odd numbers increase by 3 (e.g. 7, 9, and 11). So, let

x = the smallest odd number

x + 2 = the second odd number

x + 4 = the largest odd number. » Read more

How to Solve Consecutive Number Problems Part 2

In the previous post, we have discussed the basics of consecutive number problems. We have learned that in word problems in Algebra, consecutive numbers usually mean numbers increasing  by 1. Consecutive even numbers and consecutive odd numbers increase by 2. So, consecutive numbers whose smallest is x are x, x + 1 and x + 2 and so on, while consecutive odd/even numbers whose smallest number is y are y, y + 2, y + 4 and so on.

In this post, we begin with the third example in the series since we already had 2 examples in the previous post.

Example 3

The sum of four consecutive numbers is 70. What are the numbers?

Solution

Let

x = first number

x + 1 = second number

x + 2 = third number

x + 3 = fourth number

Since we are talking about the sum of the four numbers, we add them. That is,

sum of four numbers = 70

x + (x + 1) + (x + 2) + (x + 3) = 70

Simplifying, we have

4x + 6 = 70

4x = 70 - 6

4x = 64

4x/4 =64/4

x = 16.

So, the smallest number is 16. Therefore, the four consecutive numbers are 16, 17, 18, and 19.

Check: 16 + 17 + 18 + 19 = 70

Example 4

The sum of 3 consecutive odd numbers is equal to 51. What are the numbers?

Solution

As we have discussed above, odd numbers increase by 2 each time (like 5, 7, 9, 11), so we let

x = first number

x + 2 = second number

x + 4 = third number

Now, we add the numbers and equate to 51.

x + (x + 2) + (x + 4) = 51

3x + 6 = 51

3x = 51 - 6

3x = 45

3x/3 = 45/3

x = 15

So the smallest odd number is 15. Therefore, the three consecutive odd numbers are 15, 17, and 19.

Check: 15 + 17 + 19 = 51

You can also view the video tutorial of the discussion above in this video. The language is in Taglish.

In the next post, we will be discussing more problems about consecutive numbers.

How to Solve Consecutive Number Problems Part 1

This is the first of the Solving Consecutive Number Series, a series of post discussing word problems about consecutive numbers.

Consecutive numbers are numbers that follow each other in order. In number problems in Algebra, consecutive numbers usually have difference 1 or 2. Below are the types of consecutive numbers,

consecutive numbers – 5, 6, 7, 8, …

consecutive even numbers – 16, 18, 20, 22…

consecutive odd numbers – 3, 5, 7, 8, …

The symbol … means that the list may be continued.

Notice that consecutive numbers always increase by 1 in each term. If we make 5 as point of reference, then, we can write the numbers above as

5, 5 + 1, 5 + 2, 5 + 3.

That means that if our first number is x, then the list above can be written as

x, (x + 1), (x + 2), (x + 3)

and so on.  » Read more

How to Solve Venn Diagram Problems Part 2

In the previous posts, the introduction and the second part of this series, we have learned the basics of Venn Diagrams as well as solving the 2-circle Venn Diagram problem. In this post, we are going to solve a more complicated problem which is composed of 3-circle Venn diagram problem.

Venn Diagram Problem

There are 100 students surveyed and asked which of the following subjects they take this semester: Mathematics, English, or Biology. Below is the result of the survey.

  • 35 responded English
  • 50 responded Mathematics
  • 29 responded Biology
  • 12 responded Mathematics and English
  • 8 responded English and Biology
  • 11 responded Biology and Math
  • 5 responded all

» Read more

Solving Equations Tutorial Videos

Solving Equations is one of the most important concepts that you should learn in order to pass the Civil Service Examinations. Equations are used as they are and they are also used in solving Word Problems. Having a good grasp in solving equations can give you good advantages.

We have already discussed solving equations, but below are the supplement videos if you are not fond of reading.

Part 1 – Solving equations ofr the form ax = b, x/a = b, ax + b = c. » Read more

How to Calculate the Area of a Triangle Part 2

We continue our discussion on how to find the area of a triangle. In the previous post, we have learned where the formula for the area of a triangle came from. We have studied that a triangle with area A, base b and height h is

A = \displaystyle \frac{bh}{2}

We continue our discussion with the third example in this series.

Example 3

What is the base of a height 7 and area 8.75 square centimeters?

Solution

A = \displaystyle \frac{bh}{2}

8.75 = \displaystyle \frac{b(7)}{2}

Multiplying both sides by 2, we have  » Read more

The Word Analogy Tutorial Series

In the previous three posts, we have discussed methods and strategies on answering word analogy questions. In this post, we are going to summarize what we have learned.

This is the Word Analogy Tutorial Series.

How to Answer Word Analogy Questions Part 1 uses double word analogy question as an example to answer basic questions on verbal analogy. It uses the strategy of putting the words in sentences in order to see the relationship easily. It also teaches a strategy like looking at the words if they are noun, verb, etc. to identify the answer.  » Read more

How to Answer Word Analogy Questions Part 2

This is the second post in the Word Analogy Tutorial Series. In the previous post, we have discussed a double word analogy question. In this post, we are going to look at a single word analogy question and discuss how to answer it. In single word analogy, we are just looking for one word, not a pair of words.

Consider the example below.

Question: [ ____ : launch] [breakfast:lunch]

Choices:

a. sandwich
b. dinner
c. eggs
d. countdown

Analysis  » Read more

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