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A salesman buys a coat at a $12.5 \%$ discount off of $\$64$. He then sells the coat at a gain of $30\%$ of his cost after allowing a $15\%$ discount on the marked price. What is the marked price, in dollars, of the coat?

 Dec 19, 2021
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To find what percent of money the salesman buys the coat for, we can say that the original price is 100% of the value.

If 12.5% is discounted, 87.5% is left to pay for.

87.5% is the same as 7/8, so we multiply 64*(7/8), which equals 56.

If he sold the coat for a profit of 30%, the amount he profited is 130% of 56
130% is also equal to 1.3, so 56*1.3=72.8

We know that a 15% discount was given, so 72.8 is only 85% of the marked price. 

we can use the equation 72.8/x=85/100, which simplifies to 72.8/x=17/20

By cross multiplying, we get 17x=72.8*20, which is also 17x=1456

By dividing both sides by 17, we get x≈$85.65

 Dec 19, 2021

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