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 = 352Isolate 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.