Integer Word Problems

Integer word problems with three unknowns involve setting up and solving a system of equations based on relationships between three integers. These problems often require finding three unknown integers that satisfy given conditions.

Here are some examples of integer word problems with three unknowns, along with step-by-step solutions:

The following diagram gives the steps to solve an integer word problem with three variables using Algebra.

Integer Word Problems
Consecutive Integers Problem
Integer Word Problems with 2 Unknowns

Integer Word Problems more than 2 Unknowns

Integer Problems With More Than Two Unknowns

Integer Problems with three unknowns are not necessarily more difficult than integer word problems with two unknowns. You just have to be careful when relating the different unknowns.

Example:
Jane and her friends were selling cookies. They sold 4 more boxes the second week than they did the first. On the third week, they doubled the sale of their second week. Altogether, they sold a total of 352 boxes. How many boxes did they sell in the third week?

Solution:
Step 1: Sentence: They sold 4 more boxes the second week than they did the first. On the third week, they doubled the sale of their second week.

Assign variables:

Let	x =	boxes sold in the first week
	x + 4 =	boxes sold in the second week
	2(x + 4) =	boxes sold in the third week

Sentence: She sold a total of 350 boxes
x + x + 4 + 2(x + 4) = 352

Remove the brackets and combine like terms
x + x + 4 + 2x + 8 = 352
4x + 12 = 352

Isolate variable x
4x = 340


Step 2: The question asks for boxes sold in the third week.
Plug x = 85 into 2(x + 4) = 178

Answer: In the third week, they sold 178 boxes.

Example:
The sum of three numbers is 12. The first is five times the second and the sum of the first and third is 9. Find the numbers.

Advanced Consecutive Integer Problems
Example:
The largest of five consecutive even integers is 2 less than twice the smallest. Which of the following is the largest integer?

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Try the free Mathway calculator and problem solver below to practice various 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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