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If there is a 20 percent discount on a TV set, calculate the percentage by which the sale price must be increased in order to get the original price.
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In this question, weβre told that the price of the TV set, which we can call the original TV price, has been discounted by 20 percent to get to a sale price.
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Which means that if we find 20 percent of the TV price and subtract, this will give us the sale price.
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It can be very tempting to think if we add 20 percent to the sale price, we would get back to the original TV price.
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But this would be incorrect, since the percentage we add to the sale price is a percentage of it and not the original TV price.
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20 percent of the smaller sale price value cannot be the same as 20 percent of the larger original TV price.
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So letβs think about this in terms of the multipliers that we can use.
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If we call the original TV price π and the sale price π, then we can write π equals 80 percent of π, since weβve taken away 20 percent of π to get to π.
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We can then write our 80 percent as a fraction, giving us π equals 80 over 100 times π.
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We can then simplify our fraction to give us π equals four-fifths times π.
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So therefore, to get from our original TV price π to our sale price π, we can write that our multiplier is four-fifths.
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So therefore, if we want to get from our sale price back to our original TV price, we can divide by four-fifths.
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And to express this in terms of a multiplication rather than a division, we can say that this is the same as multiplying by five over four.
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We can do this because when we divide by a fraction, we change the division to a multiplication and we flip the numerator and denominator.
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So now we have worked out that to get from our sale price to our original TV price, we multiplied by five-fourths.
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But we need to express this as a percentage.
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To do this, we write our multiplier five-fourths times 100, giving us 500 over four, which we can write as 125 percent.
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Since this value 125 percent also includes the 100 percent of the sale price, then we must subtract 100 percent to give us 25 percent.
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So we can say that the percentage by which the sale price must be increased to get the original price is 25 percent.