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asked • 06/12/14

One number is 200% greater than the other and their difference is 20. What is the smallest number?

it is about math and algebra please solve 

J M.

Sorry I realize it’s 8 years later but as I’m trying to determine the simplest method to calculate the % increase in my energy bill I did a quick search to make sure I was doing it correctly. Viewing the information here slightly confused me. I was taught to use algebra in this scenario where 200%x - x = 20. But wouldn’t one simply move the decimal when calculating with percentages? Then it’s simply: 2.00x-x=20 or x=20 Therefore the smaller number is 20 and 200% of 20 is 40. The story checks out since 40 minus 20 would be 20. Lol my apologies I have spent too much time viewing this calculation but both Arthur & Bob’s equations lead to the smaller number being 10, and I know that a 200% increase of 10 is 30, but also 200% of 10 is 20. So the wording in my head for the original question is 200% of the smaller number less the smaller number equals 20. See how I’m at a loss? I’m thinking maybe we would arrive at the correct number if all 3 of us read the text of the question from its original source. Either way cheers. 🍻 the calc for % increase is here. New Price - Old Price = Difference (Difference/Old Price) x 100 = % Or $440- $370=$70 70/370 = .1892 .1892 x 100 = 18.92% increase in energy costs.
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09/07/22

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Bob A. answered • 06/12/14

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B = bigger, S = smaller
 
First you need to be careful with % to see if it is 200% of ( B = 200% S ) where the total of B is 200%.  Or if it is 200% bigger ( B = S + 200% S ) where the difference is 200%.

One number is 200% greater than the other
gives   B = S + 200% S
 
their difference is 20
gives   B - S = 20
 
Can you solve these two simultaneous equations now to find S?
B = S + 200% S = S + 2.00•S = 3•S
B - S = 20 => B = 20 + S
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