The Math Store, a very popular outlet, bought 400 calculators at $28 less 7.5%, 3%. The markup on the calculators was 35% of the selling price.  After selling 50% of the shipment, the rest of the calculators were marked down to a reduced selling price. When there were only 20 calculators left, the Math Store marked these down to $15.90.

Round your final answers properly to two decimal places:

a)  What is the cost for each calculator (C) ?

$ ____________ 

b)  What is the Total Cost (TC)?

$  ____________ 

c)  What is the regular selling price for the calculators?

$  ____________ 

d)  Given an average markup of 25% based on sales, what was the total sales?

$  ____________ 

e)  Given the total sales above,  what was the reduced price of the calculators?

$  ____________ 

Expert Answers

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(a) The cost for each calculator is $28(1-.075)(1-.03)=$25.12

(b) The total cost for the shipment is $25.12(400)=$10,048 (Using the rounded figure. Unrounded we get $10,049.20)

(c) The original selling price had a markup of 35%, based on selling price. If S is the selling price then

` (S-25.12)/S=.35 ` so `S=25.12/.65=38.65 ` so the selling price was $38.65

(d) Given an average markup of 25% based on sales, we have (TS is total sales) ` (TS-10048)/(TS)=.25`

Then `TS=10048/ ` so the total sales were $13,397.33

(e) The total sales are found by TS=200(38.65)+180(RP)+20(15.90) where RP is the reduced price. We have the sum of the calculators sold at regular retail, the calculators sold at the reduced price, and the last 20 calculators sold at the clearance price.

So 13,397.33=7730+180(RP)+318 ==>

The reduced price was $29.72

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