how much did it cost

Question

Ms Arias buys wool, makes fabric out of it, adds 25% to the cost of the wool, and sells it to Mr. Bau. Mr. Bau takes the fabric, makes a coat out of it, adds 25% to the cost of the fabric and sells it to Ms Cho. Ms Cho is a wholesaler. She finds a buyer, transports the coat, adds 25% to the cost of the coat, and sells it to Mr. Duran. Dr. Duran is a retailer. He advertises it, displays it in a store, adds 25% to the cost of the coat, and sells it to Ms Edwards, who wears it. If Ms Edwards paid $100 for the coat, how much did the wool for the coat cost?

Answer 1

 

We add 25% 4 times during the process

Arias → Bau

Bau → Cho

Cho → Duran

Duarn → Edwards

 

Final cost $100

 

Retail cost = 1.25ⁿW

Where n = number of sales/steps

W = original price of the wool

 

100 = 1.25⁴W

W = 100/1.25⁴

W = $40.96

 

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you can work this out step by step

A buys the wool at cost W

A sells it to B at 1.25W

B sells it to C at 1.25(1.25W)

C sells it to D at 1.25(1.25)(1.25W)

D sells it to E at 1.25(1.25)(1.25)(1.25W)

100 = 1.25⁴W