How to Solve Number Word Problems Part 3

This is the third part of The Number Word Problem Series. In this post, we will be solving number word problems about consecutive numbers.  In number word problem solving, consecutive numbers are numbers that follow each other in order.  Here are the examples of consecutive numbers (integers).

consecutive numbers: 4, 5, 6, 7, 8, …

consecutive odd numbers: -2, 0, 2, 4, …

consecutive odd numbers: 7, 9, 11, 13, 15, …

I am quite sure that you have solved consecutive numbers in your high school mathematics class.

In the previous post, we finished our 6th problem, so, we start with the seventh problem.

Problem 7

The sum of two consecutive numbers is 69. What are the two numbers?

Scratch Work

If 7 is a number, then the next consecutive number is 7 + 1. Therefore, if two numbers are consecutive and the smaller number is x, then the next number is x + 1. Their sum is 69. This means that if we add x and x + 1, the result is equal to 69. From there, we can now form our equation.

Solution

Let x be the smaller number and x + 1 be the larger number.

x + (x + 1) = 69

2x + 1 = 69

Subtracting 1 from both sides, we get

2x = 68

Dividing both sides by 2, we get

x = 34.

Therefore, the smaller number is 34 and the larger number is 34 + 1 = 35

Check: 34 + 35 = 69.

Problem 8

The sum of three odd consecutive numbers is 63. What are the three numbers?

Scratch Work

Please take note that we are talking about odd numbers. So, if the smallest number is, say, 7, the next odd number is 7 + 2 = 9. The next odd number is 7 + 4 = 11. So, if the smallest number is x, we have

x + 2: next odd number

x + 4: largest odd number

Now, if you add these three numbers, the sum will be 63.

Solution

Let x, x + 2, and x + 4 be the consecutive odd numbers.

x + (x + 2) + (x + 4) = 63

3x + 6 = 63

Subtracting 6 from both sides we have

3x = 57

Dividing both sides by 3, we have

x = 19.

So, the numbers are 19, 19 + 2 = 21 and 19 + 4 = 23.

Check: 19 + 21 + 23 = 63.

Problem 9

The sum of three even integers is 60. What are the three numbers?

Scratch Work

Observe from the introduction above, the consecutive even numbers also increase by 2 everytime. So, if the smallest number is x, then the other larger numbers are x + 2 and x + 4.

Solution

x + (x + 2) + (x + 4) = 60

3x + 6 = 60

Subtracting 6 from both sides of the equation results to

3x = 54

Dividing both sides by 3, we have

x = 18.

Therefore, the three numbers are 18, 18 + 2= 20, and 18 + 4 = 22.

Check: 18 + 20 + 22 = 60.

In the next post, we will solve various number problems particularly those with fractions.

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