Integer Word Problems

Integer word problems are word problems that involves integers and how they are related according to the question.

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 = 2a –5
        and not j = 5 – 2a

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.

We will cover some examples with two unknowns and more than two unknowns. Think carefully when you assign the variables to the unknowns. Another type of integer problems is the consecutive integer problems.

Integer Problems With Two Unknowns

Example 1:

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

Isolate variable x

Answer: The team lost 5 games.

Example 2:

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 marbles

Sentence: Initially, blue marbles = red marbles = x, then John took out 5 blue marbles.
x – 5 = blue marbles

Sentence: twice as many red marbles as blue marbles in the bag
x = 2(x –5)

Step 2: Solve the equation

x = 2(x –5)

Remove the brackets
x = 2x – 10

Isolate variable x
x = 10

Answer: There are 10 red marbles in the bag.

The following video gives another example of integer word problems.

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