Question

A sporting goods store is having a sale in which all sleeping bags are discounted by 20%. Priya has a coupon for $5 off the regular price of a sleeping bag. The store first applies this coupon and then takes 20% off the reduced price. If Priya pays $34.40 for the sleeping bag, what was the original price, x, before the sale and without the coupon?

Answer 1

the original price was "x", which oddly enough is the 100%.

now, let's pluck out of "x" 5 bucks, so that makes it "x-5", that's our new adjusted 100%, from which the lady at the counter is happy to apply a 20% discount. Now, if the lady discounts 20% off of that "x-5" amount, what Priya is really paying for the sleeping bag is just 100% - 20% = 80%, and we happen to know that that 80% was really $34.40.

now, if "x - 5" is the 100%, and we know that 34.40 is the 80%, what the heck is "x"?

`\begin{array}{ccll} amount&\%\\ \cline{1-2} x-5 & 100\\ 34.40& 80 \end{array} \implies \cfrac{x-5}{34.40}~~=~~\cfrac{100}{80} \implies \cfrac{ x-5 }{ 34.40 } ~~=~~ \cfrac{ 5 }{ 4 } \\\\\\ 4x-20=172\implies 4x=192\implies x=\cfrac{192}{4}\implies x=48`