A merchant purchased a line of handbags for 30$ each. She wanted to offer a 10% discount off the listed selling price and still make a 20% p

Question

A merchant purchased a line of handbags for 30$ each. She wanted to offer a 10% discount off the listed selling price and still make a 20% profit. What price should she mark on the label?

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Rose 1 week 2021-11-25T09:46:06+00:00 1 Answer 0

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    2021-11-25T09:48:01+00:00

    The merchant spent 30$ to buy the bag. 20% of this price is

    \dfrac{20}{100}\cdot 30=6

    So, he has to sell the bag at 36$.

    This is not the selling price, but its 90%, because of the 10% discount.

    So, the label price is such that

    \dfrac{90}{100}x=36 \iff x=\dfrac{3600}{90}=40

    So, the merchant will declare a price of $40.

    After the 10% discount, the price will drop to $36.

    If she sells the bag for $36, her profit will be $36 – $30 = $6, which is 20% of 30 as required.

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