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.
$90
$100
$120
$140
$150
Continue
Continue
