# Problem of the week #93 - January 6th, 2014

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#### Jameson

##### Administrator
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At a certain store in New York City all items are on sale at a discount of 20% of the normal price. A young woman finds a dress she likes that is also an additional 20% off. The sales clerk is quite tired and when ringing up the bill for the young woman takes off 40% of the original price for the dress - a mistake.

If the original price for the dress was \$2014, by how much did the sales clerk accidentally undercharge? -------------------- Remember to read the POTW submission guidelines to find out how to submit your answers! #### Jameson ##### Administrator Staff member Congratulations to the following members for their correct solutions: 1) MarkFL 2) magneto 3) Deveno 4) anemone Solution (from magneto): Suppose the dress's original price is$x$. Since it was discounted twice at$20\%$, the actual sales price is$(0.8)(0.8)x = 0.64x$(as it retains$80\%$of the value at each discount.) If the dress was discounted at$40\%$, the actual sales price would be$0.6x$. Note the difference is$0.04x$. If$x = 2014$, the clerk would have undercharged$(0.04)\times \$2014 = \$80.56\$.

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