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.
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?
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.
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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