Algebra Word Problems: Integers
Related Topics:
Integer word problems with more than two unknowns
Consecutive integer problems
More Algebra Word Problems
Integer word problems with two unknowns involve setting up and solving a system of equations based on relationships between two integers. These problems often require finding two unknown integers that satisfy given conditions.
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.
The following diagram gives the steps to solve an integer word problem with two variables using Algebra.
Key Steps for Solving Integer Word Problems with Two Unknowns:
- Define variables clearly: State what each variable represents.
- Set up two equations: The problem will give you two pieces of information, allowing you to create two equations.
- Solve the system of equations: Use substitution, elimination, or other methods.
- Check your answers: Make sure your answers are integers and make sense in the context of the problem. If you get non-integer results, double-check the problem for typos or errors.
Integer Word Problems
Consecutive Integers Problem
Integer Word Problems with 2 Unknowns
Integer Word Problems more than 2 Unknowns
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 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.
Check out other Algebra Word Problems
Age Word Problems, Average Word Problems, Coin Word Problems, Consecutive Integer Word Problems, Digit Word Problems, Distance Word Problems, Fraction Word Problems, Geometry Word Problems, Integer Word Problems, Interest Word Problems, Lever Word Problems, Mixture Word Problems, Money Word Problems, Motion & Distance Word Problems, Number Sequence Word Problems, Proportion Word Problems, Quadratic Equation Word Problems, Ratio Word Problems, Symbol Word Problems, Variation Word Problems, Work Word Problems.
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