Question 184096
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Let <i>w</i> be the wholesale price and <i>M</i> be the retail mark-up expressed as a decimal fraction.


The buying club sells for *[tex \Large w + 0.08w]


The retail store sells for *[tex \Large w + Mw - 0.1(w + Mw) = 0.9(w + Mw)]


It is less expensive to buy through the club if:



*[tex \LARGE \text{          }\math w + 0.08w < 0.9(w + Mw)]


So:


*[tex \LARGE \text{          }\math w + 0.08w < 0.9w + 0.9Mw]


*[tex \LARGE \text{          }\math w + 0.08w - 0.9w < 0.9Mw]


*[tex \LARGE \text{          }\math 0.18w < 0.9Mw]


*[tex \LARGE \text{          }\math \frac{0.18w}{0.9w} < M]


*[tex \LARGE \text{          }\math 0.2 < M]


Hence, if the retail store markup is greater than 20%, it is less expensive to buy from the wholesale buying club.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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