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A bottle of hand lotion is on sale for five dollars and one cent.
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If this price represents a twenty-eight percent discount from the original price, determine the original price to the nearest cent.
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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.
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To simplify what we have, we can take one hundred and subtract twenty-eight to get seventy-two percent.
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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.
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We can replace seventy-two percent with a decimal.
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We need to take seventy-two, divide by one hundred, and get rid of the percentage sign.
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That is equal to zero point seven two.
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We can also replace the word original with a variable 𝑥.
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This way, we can solve for the original price and then also get rid of the dollar sign.
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So it equals five point zero one.
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So in order to solve for 𝑥, we need to divide both sides by zero point seven two.
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And we get six point nine five eight.
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Now we need to round to the nearest cent.
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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.
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In order to make that decision, we need to look at the eight.
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Since eight is five or greater, it will round the five up to a six.
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So 𝑥 is equal to six point nine six.
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Therefore, the original price is six dollars and ninety-six cents.