Percents: Overview
Real-estate salesman Z is selling a house at a 20% discount from its retail price. Real-estate salesman X vows to match this price and then offers an additional 10% discount. Real-estate salesman Y decides to average the prices of salesmen Z and X and then offer an additional 25% discount. Salesman Y's final price is what fraction of salesman X's final price?
Correct.
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Z offers a 20% discount on the house, so he's offering it for $80.
X matches the offer of $80, then offers another 10% discount. Careful here—X's additional discount is calculated from his matching offer of $80, not from the original! Thus, X offers an additional $$10\% \times $80 = $8$$ discount, and his final price is $72.
Along comes Y, averages X's and Z's price, and then offers a 25% discount on the new price. The average of 80 and 72 is
>$$\frac{80+72}{2} = \frac{152}{2} = 76$$.
We then calculate that 25% of 76 is
>$$\frac{25}{100} \times 76 = \frac{1}{4}\times 76 = 19$$.
Thus, Y's final price is $$76-19 = 57$$.
Place Y's price over X's price to find the fraction: $$\frac{57}{72}$$. Reduce by 3 to get to $$\frac{19}{24}$$.
Incorrect.
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Incorrect.
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Incorrect.
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This is the fraction of X's from the original retail price. However, what did the question ask?
Incorrect.
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$$\frac{72}{80}$$
$$\frac{72}{100}$$
$$\frac{57}{80}$$
$$\frac{19}{24}$$
$$\frac{76}{100}$$
