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Bell Work You are the head supervisor at the Shoe Department in Cleveland, Ohio. As tax season has arrived, you are trying to examine the commission amount for each salesman for this month to file your taxes accurately. Here is what we know… Leigh sold $5,200 in mens shoes, $4,200 in womens shoes, and $2,300 in childrens shoes. Khalid sold $8,100 in mens shoes, $8,400 in womens shoes, and $3,100 in childrens shoes. Ari sold $2,700 in mens shoes, $7,400 in womens shoes, and $630 in childrens shoes. This months commission rate is 9.5% for mens sales, 10% for womens sales, and 12% for childrens sales. How do we begin to solve this problem?

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Step One: Organize Data Sales Name Sales in Mens Shoes Sales in Womens Shoes Sales in Children s Shoes Leigh$5,200$4,200$2,300 Khalid$8,100$8,400$3,100 Ari$2,700$7,400$630 Commission Rate Mens Sales9.5% Womens Sales 10% Childrens Sales 12%

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Step Two: Create Matrices Dimensions ?

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Step Three: Multiply Matrices Step Four: Analyze Results What does each number represent in our matrix product? Who earned the most in commissions? How do you know? Who earned the least?

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Lets Try Another Problem! Students collected recyclables for fund-raising over a 3-week period. Use what you know about matrix operations to find the total amount of money collected for each type of item. Heres what we know about the quantity of each item recycled… On week 1, students collected 29 pounds of glass. On week 2, students collected 25 pounds of glass. On week 3, students collected 16 pounds of glass. On week 1, students collected 8 pounds of cans. On week 2, students collected 11 pounds of cans. On week 3, students collected 6 pounds of cans. On week 1, students collected 163 pounds of newspapers. On week 2, students collected 127 pounds of newspapers. On week 3, students collected 206 pounds of newspapers. On week 1, students collected 53 pounds of office paper. On week 2, students collected 107 pounds of office paper. On week 3, students collected 84 pounds of office paper.

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Heres what we know about the earnings… During the first week, students earned $0.02 per pound for glass, $0.70 per pound for cans, $0.02 per pound for newspaper, and $1.06 per pound for office paper. During the second week, students earned $0.02 per pound for glass, $0.55 per pound for cans, $0.01 per pound for newspaper, and $1.00 per pound for office paper. During the third week, students earned $0.01 per pound for glass, $0.42 per pound for cans, $0.02 per pound for newspaper, and $1.03 per pound for office paper.

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Step One: Organize Data

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Step Two: Create Two Matrices

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Step Three: Multiply Matrices Step Four: Analyze Results Homework! Which values matter in this matrix product? How come the other values dont matter? How much did we earn from glass? Cans? Newspapers? Office Paper? How much did the students earn total?

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