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

[Jameson]

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?
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[Jameson]

Congratulations to the following members for their correct solutions:

1) MarkFL
2) magneto
3) Deveno
4) anemone

Solution (from magneto):

Spoiler

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 $(0.04)\times \$2014 = \$80.56$.