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Reverse Plugging In: Hard to Spot RPI Situations

A retailer sells pashminas at a 10% discount. If a pashmina cost him $75 and he wants to make a profit of no less than 20% on the cost (after the discount), then what is the minimum tag price he needs to put on a pashmina?
__Alternative Method__: Do a straightforward calculation. Form the following equation: >$$\text{Cost}+ 20\% \text{ profit} = \text{Tag price} - 10\% \text{ discount on the tag price}$$. >$$\displaystyle $75 +0.2 \times $75 = \text{Tag price} - 0.1 \times \text{Tag price}$$ >$$$75 + $15 = 0.9 \times \text{Tag price}$$ >$$$90 = 0.9 \times \text{Tag price}$$ >$$\displaystyle \frac{$90}{0.9} = \text{Tag price}$$. Therefore, the tag price is >$$\displaystyle \text{Tag price} = \frac{$90}{0.9} = $90 \div \frac{9}{10} = $90 \times \frac{10}{9} = $100$$.
Incorrect. [[Snippet]] If the tag price is $90, then the customer will pay 10% less after the discount, so the customer will pay >$$90 - 10\% \text{ of } $90 = 90 - 9 = $81$$. If the customer pays $81 for a pashmina that cost the retailer $75, then >$$\text{Profit} = 81 - 75 = $6$$. Now, find out what percent 6 is of the retailer's cost. >$$\displaystyle \text{Percent} = \frac{$6}{$75} \times 100 = \frac{2}{25} \times 100 = 2 \times 4 = 8\%$$ Eliminate this answer choice because the retailer will not sell for less than 20% profit.
Incorrect. [[Snippet]]
Incorrect. [[Snippet]]
Incorrect. [[Snippet]]
Correct. [[Snippet]] If the tag price is $90, then the customer will pay 10% less after the discount, or >$$90 - 10\% \text{ of } $90 = 90 - 9 = $81$$. If the customer pays $81 for a pashmina that cost the retailer $75, then the profit will be >$$\text{Profit} = 81 - 75 = $6$$. Now, find out what percent 6 is of the retailer's cost of $75: >$$\displaystyle \text{Percent} = \frac{$6}{$75} \times 100 = \frac{2}{25} \times 100 = 2 \times 4 = 8\%$$ Since $6 is less than 20% of the retailer's cost of $75, the profit is too low. Eliminate answer choice A, and __Plug In__ B:
If the tag price is $100, then the customer will pay 10% less after the discount, or >$$100 - 10\%$$ of $$100 = 100 - 10 = $90$$. If the customer pays $90 for a pashmina that cost the retailer $75, then the profit will equal >$$\text{Profit} = 90 - 75 = $15$$. Now, find out what percent 15 is of the retailer's cost of $75: >$$\displaystyle \text{Percent} = \frac{15}{75} \times 100 = \frac{1}{5} \times 100 = 20\%$$. This is the correct answer since the retailer can make the least required profit (20%) by setting a tag price of $100.
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