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

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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