Merchandise and Compound Interest Problems

[neomah]

Merchandise Problems

Hello again!

I have couple more questions that I need to be clarified:

Merchandise:/Mardown Problem:

A lawn mower retails for $349. The dealer's overhead is 25% of cost, and normal operating profit is 16⅔ % of cost.

a) What is the largest amount of markdown that will allow the dealer to break even? For full marks your answer(s) should be rounded to the nearest cent. ANS: $41.06

b) What rate of markdown will price the lawn mower at cost? Note: Please make sure your final answer(s) are in percentage form and are accurate to 2 decimal places. ANS: 29.41%
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What I did:

A) M = E + P
=0.25C + 0.1666666C
M = 0.4166666C

S = C + M
= C + 0.4166666C
S = 1.4166666C

Markdown% = Profit
Markdown% = 0.1666666C

Markdown $ = 0.16666666C / 1.416666666C
=0.117647 * 349
=$41.06

I got this part right, but when I try to solve B...

B) MD% = 41.06 / 1.41 = 29.12%?

I keep getting 29.12% instead of the 29.41%? Can someone please clarify this? Thank you!

 

[Ishuda]

There is a difference between breaking even (your price includes overhear) and at cost (you don't even make your overhead), so the 41.06 is incorrect. Also that 1.41 in the denominator should be 1.41 C to make sure both numerator and denominator are both the same units (dollars in this case). You were just lucky that the numbers came as close as the did.

Selling the lawn mower at cost means
S - MD = C
and percentage markdown is
MD% = 100 * MD / S