Integer Word Problems

In another lesson, we have looked at some examples of Integer Word Problems that involve two unknowns. In this lesson we will look at Integer Word Problems that has more than two unknowns.

Integer Problems With More Than Two Unknowns

These problems 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.

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