Integer word problems are word problems that involves integers and how they are related according to the question. Think carefully when you assign the variables to
the unknowns.

### Integer Problems With Two Unknowns

Example 1:

Example 2:

The following videos give more examples of integer word problems.

Example: One number is four more than a second number. If their sum is 38, find the two numbers.
Example: The larger of two integers is seven more than the smaller integer. Their sum is 49. Find the integers.

Example: Two numbers add up to 51. Find the two numbers if they are 5 units apart.
Example: An integer is one less than twice that of another. If their sum is 20, find the integers.

Example: The sum of two numbers is 17. Three times one number is one more than twice the other.
Example:

(1) The sum of two numbers is 30. Twice the smaller number is half the larger number. Find the numbers.

(2) The sum of three consecutive odd integers is 15. What is the largest integer?

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Things to watch out for: be careful when translating the sentences into equations.

For example:

“John has 5 fewer sweets than twice the number that Alice has”

is translated as *j* = 2*a* –5

and not *j* = 5 – 2*a*

Although, the number 5 is mentioned first in the sentence that does not
mean that it would come first in the equation. Read the sentence carefully.

In these lessons, we will cover some examples of integer word problems with two unknowns. Refer to the following related topics for other types of integer word problems.

Related Topics:

Integer word problems with more than two unknowns,
Consecutive integer problems,
More Algebra Word Problems

A team won 3 times as many matches as it lost. If it won 15 matches, how many games did it lose?

Solution:

Step 1: Sentence: A team won 3 times as many matches as it lost.

Assign variables:

Let x=matches lost 3x=matches won Sentence: It won 15 matches

3x =15

Step 2: Solve the equation

Answer: The team lost 5 games.Isolate variable

x

Initially, there were the same number of blue marbles and red marbles in a bag.

John took out 5 blue marbles and then there were twice as many red marbles as blue marbles in the bag. How many red marbles are there in the bag?

Solution:

Step 1: Assign variables:

Let

x= red marblesSentence: Initially, blue marbles = red marbles =

x, then John took out 5 blue marbles.

x– 5 = blue marblesSentence: twice as many red marbles as blue marbles in the bag

x= 2(x–5)

Step 2: Solve the equation

Answer: There are 10 red marbles in the bag.

x= 2(x–5)Remove the brackets

x= 2x– 10Isolate variable

x= 10

x

Example: One number is four more than a second number. If their sum is 38, find the two numbers.

Example: The sum of two numbers is 17. Three times one number is one more than twice the other.

(1) The sum of two numbers is 30. Twice the smaller number is half the larger number. Find the numbers.

(2) The sum of three consecutive odd integers is 15. What is the largest integer?

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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