A company manufactures headphones for $35. They want to make a 24% profit. How much do they need to charge to make their desired profits?

A company manufactures headphones for $35. They want to make a profit of 24%, so they want to know how much they should charge for the headphones.
 
One way to approach this problem is to reason that if 24% of the price is profit, then 76% of the price covers the cost. Then if r is the retail price we have 76% of r is $35.
.76r=35 ==> r=$46.05
 
Another approach is to use the equation cost = retail times the cost complement where cost is the cost to manufacture, retail is the selling price and the cost complement is the percentage of the selling price devoted to covering the cost. The cost complement is 1-(profit percent).
So here we would have 35=r*.76 so r is 46.05 again.
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In order to have a 24% profit, the company should sell the headphones for $46.05
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