## 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.