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 . . .
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 $A-\frac{p}{100}A$.
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.
And the answer is
$$\frac{45-20}{45}.100\% \approx 55.55 \% \approx 56 \% $$
Well, if A is $x$ percent less than B, it means $ x=\frac{B-A}{B} $ or $ A = (1-x)\cdot B $.
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%
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.
