Farmer A and Farmer B each own apple orchards. They had a contest to see who could sell the most apples. Their contest ran from September 15 through October 15. During the first week, Farmer A sold half as many boxes as Farmer B, but during the second week, he sold three times as many as Farmer B. During the third week, Farmer A sold half as many as Farmer B sold during the same week. During the last week of the contest Farmer A sold five times as many boxes as Farmer B. In total, Farmer A sold 30 more boxes of apples than Farmer B, and together they sold 162 boxes. How many boxes did each of them sell each week of the contest? Using words, numbers, or pictures or all three, explain in detail how you found your answer.

(Hint: Farmer A sold 11 boxes during week 1.)