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.
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.
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 Alegebra 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
Isolate variable x
Answer: The team lost 5 games.
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 marblesSentence: 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 – 10Isolate variable x
x = 10
Answer: There are 10 red marbles in the bag.