A bottle of hand lotion is on sale for five dollars and one cent. If this price represents a twenty-eight percent discount from the original price, determine the original price to the nearest cent.
The original price would represent one hundred percent of the cost, and twenty-eight percent represents the discount, so we wanna take away twenty-eight percent of the original cost, which would give us the sale price of five dollars and one cent. To simplify what we have, we can take one hundred and subtract twenty-eight to get seventy-two percent.
This means if you take away twenty-eight percent of the original cost, you’re actually paying seventy-two percent of the original price, which is our discounted price of five dollars and one cent. We can replace seventy-two percent with a decimal. We need to take seventy-two, divide by one hundred, and get rid of the percentage sign.
That is equal to zero point seven two. We can also replace the word original with a variable 𝑥. This way, we can solve for the original price and then also get rid of the dollar sign.
So it equals five point zero one. So in order to solve for 𝑥, we need to divide both sides by zero point seven two. And we get six point nine five eight. Now we need to round to the nearest cent. That means we must round two decimal places, so we need to decide whether to keep the five a five or round it up to a six.
In order to make that decision, we need to look at the eight. Since eight is five or greater, it will round the five up to a six. So 𝑥 is equal to six point nine six. Therefore, the original price is six dollars and ninety-six cents.