Percent Puzzle!
If x = 8 0 % , then by what percent is x larger than x 2 ?
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3 solutions
Why x^2 is 64%
why did u subract and divide 64%
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To get ratio or fraction of increase to the original number!
80% = 0.8. if x =0.8, x 2 =0.64 (which is equal to 64%). 0 . 6 4 0 . 8 = 6 4 8 0 = 4 5 =1.25=125%. if 80% ( x ) is 125% of 64% x 2 , then x is 25% more than x 2 .
Here the question is "What percent is 0.64 smaller than 0.8?". The basis of the comparison would have been 0.8.
Moderator note:
This solution does not answer the question.
The question is "by what percent is x larger than x 2 "?
That is not what the question asks for. It asks for "what percent is x larger than x 2 ? ".
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i don't get why the denominator needs to 0.64 and not 0.8
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Because in other words, the question asks for how much percent 80% is larger than 64%. So if we are going from 64 to 80 we need to add 16, but, how much is 16 compared to what I had in the first place? Thus the 16/64.
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@Andrei Ce – That's correct. In such a problem, you have to correctly identify what the initial value is. When we say "How much is A larger than B", then B is our basis of comparison, which is why it goes into the denominator.
Similarly, for the question "How much has the population grown in 2015 from the year 2010?", the basis is "from the year 2010", which forms the denominator.
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@Calvin Lin – got it now!thanks u both
@Calvin Lin – So if I wanted to say: How much percent is 64% smaller than 80%, I would go from 80 to 64, 16, and I have 80 in the first place, so the answer becomes: 16/80 ???
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@Apurv Potter – What is the initial value and what is the final value? That will tell you what the basis of comparison is.
@Andrei Ce – So if I wanted to say: How much percent is 64% smaller than 80%, I would go from 80 to 64, 16, and I have 80 in the first place, so the answer becomes: 16/80 ???
Why can't the answer be 16%? x=0.8, x^2=0.64, 16%=0.16. 0.8 is 0.16 more than 0.64.
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Because when the question asks "by what percent", it means [final - initial ] / [initial]. We want to find the percentage difference, and not the difference as expressed in percentages.
x = 8 0 % , so x 2 = 6 4 % . Thus, x is larger than x 2 by 6 4 % 8 0 % − 6 4 % = 6 4 % 1 6 % = 4 1 = 2 5 % .