# Need help visualizing this percentage problem

Ok i understand how the answer is calculated

R :: 40*.5 = 20 television sets T :: 50*.9 = 45 television sets

45*x = 20 x = 0.44 or 44%

so R sold 44% of what T sold but it's asking "what percent less" ? i know the answer is 56% which is 1 - .44 = .56 or 56% but i'm having trouble grasping what it actually means by what percent less . . .

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Well, think about a drink that has 75% less Calories. If it had 500 Calories before, then the diet edition has 75% taken off of it(off the fat edition): 500·0.25=125 Calories in the diet edition. – Hex4869 Sep 9 '14 at 7:07

You probably know what it means to say that the number $x$ is 12 less than the number $y$: It means $x$ is $y-12$ (which can be read as y less 12). Something is p percent less than $A$ if it's A less p percent (of A), or $A-\frac{p}{100}A$.

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Look at the chart "Number of Units Sold as a Percent of Number of Units in Stock":

The number of television sets sold by Store R last month was approximately 50% $(0.5)$ of its number of television sets in stock, which is: $0.5*40 = 20$.

The number of television sets sold by Store T last month was approximately 90% $(0.9)$ of its number of television sets in stock, which is: 0.9*50 = 45.

And now, the original question is equivalent to: "20 is approximately what percent less than $45$".

To compute A is what percent less than B, we compute $$\frac{\mathrm{difference}}{\mathrm{base}}$$ , where difference is B-A (since A is less than B), and base is B.

$$\frac{45-20}{45}.100\% \approx 55.55 \% \approx 56 \%$$

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Well, if A is $x$ percent less than B, it means $x=\frac{B-A}{B}$ or $A = (1-x)\cdot B$.

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Basically, you already figured out that store R sold 20 TV sets and store T sold 45 TV sets. Store T - Store R = The number that store R sold less than store T = 25

You want to divide the difference by the original. 25/45 = .555 or 56%

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if store R sold 44% of what store T sold, then it was 56% less than the total sold by T.

20/45 = .44

Imagine, how much percentage would store R need to increase to sell the same amount as store T (i.e. 100% of what store T sold). It would need to increase sales by 56% percent to get to 100%.

1-.44 = 56%.

Steve Kass's answer is sufficient, but that is how I now see it.

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