Need Algebra Help
 04-03-2015, 05:43 PM #1 Give me a museum and I'll fill it. (Picasso)Give me a forum ...   Join Date: Jun 2006 Posts: 11,407 Need Algebra Help y = 176091[x(-1.126)] Can someone help me get this into x= format? This is for converting a book's Amazon sales ranking into an estimate of sales per day. __________________ __________________ Al
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 04-03-2015, 05:53 PM #2 Recycles dryer sheets   Join Date: Dec 2003 Posts: 456 Not sure what your expression means, Al. Is it: y = 176091 times x to the power -1.126 ? That is y= 176091*(x^-1.126) ? Or .... ? __________________
 04-03-2015, 05:54 PM #3 Thinks s/he gets paid by the post   Join Date: Jan 2011 Posts: 1,317 y=176091[x(-1.126)] y/176091= x(-1.126) (y/176091)/-1.126=x
 04-03-2015, 06:12 PM #4 Recycles dryer sheets   Join Date: Dec 2012 Posts: 424 To add on to mystang52 (y/176091)/-1.126=x (y/176091)X(-1/1.126)=x -y/198278.466=x At least I think it's right.
 04-03-2015, 06:18 PM #5 Recycles dryer sheets   Join Date: Dec 2003 Posts: 456 The only thing that bothers me about Elbata's and mystang's solution is that positive y gives negative x, and vice versa. Since the equation is supposed to be converting sales ranking into sales per day, that doesn't sound right. (You can't have negative sales, or negative rankings.) That's why I was guessing that an exponent must be involved. Waiting for Al to comment ....
 04-03-2015, 06:22 PM #6 Recycles dryer sheets   Join Date: Dec 2012 Posts: 424 I see what you're saying Peter, I was just having fun using math that I've learned from Khan Academy.
 04-03-2015, 06:33 PM #7 Thinks s/he gets paid by the post   Join Date: Aug 2006 Posts: 2,366 If the original equation is written (correctly?) as Peter states, the solution is x = (y/176091)^1.126 The other solutions give a negative number for x which doesn't make any sense since y is positive. __________________ I'd rather be governed by the first one hundred names in the telephone book than the Harvard faculty - William F. Buckley
04-03-2015, 06:33 PM   #8
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Quote:
 Originally Posted by Elbata I see what you're saying Peter, I was just having fun using math that I've learned from Khan Academy.
+1 Just followed thru on the algebra. I figured the - was a typo. Or, if it was an exponent...............then my algebra memory is gone for that aspect.

 04-03-2015, 06:43 PM #9 Thinks s/he gets paid by the post   Join Date: Jul 2007 Posts: 1,596 Not a direct answer to your question but if the number 176091 is a book sales ranking on Amazon then the sales is likely less than one a day. As I recall a sales ranking of between 50k and 100K meant sales of about 1 book a day.
04-03-2015, 06:48 PM   #10
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Quote:
 Originally Posted by Peter Not sure what your expression means, Al. Is it: y = 176091 times x to the power -1.126 ? That is y= 176091*(x^-1.126) ? Or .... ?
I've got to think that y = 176091*(x^-1.126) is the intended formula. It passes a reasonableness check for being a sensible relationship between sales ranking and number of sales per day that the other formula doesn't.

If that's the correct formula, then my calculations indicate that the formula for expressing x as a function of y is

x = 45576 * ( y ^ -.8881)

04-03-2015, 06:55 PM   #11
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Quote:
 Originally Posted by zinger1457 Not a direct answer to your question but if the number 176091 is a book sales ranking on Amazon then the sales is likely less than one a day. As I recall a sales ranking of between 50k and 100K meant sales of about 1 book a day.
Assuming x is being raised to the -1.126 power, a sales ranking of 50,000 would mean

y = 176091 * (50000 ^ -1.126) = 0.9 sales per day

Similarly, a sales ranking of 100,000 would mean

y = 176091 * (100000 ^ -1.126) = 0.4128 sales per day

Those numbers aren't too far off from your recollection of about 1 sale per day for sales rankings in the 50,000 - 100,000 range.

 04-03-2015, 07:10 PM #12 Thinks s/he gets paid by the post   Join Date: Feb 2011 Location: Triangle Posts: 3,219 Part of what makes it confusing is that there was no explicit statement of what x and y are. I suppose y is sales per day (the thing being solved for) and x is the sales rank. The constants - were they given by Amazon? The notation is a little odd. But I guess karluk has it right. __________________
 04-03-2015, 08:32 PM #13 Thinks s/he gets paid by the post   Join Date: Jul 2005 Posts: 3,877 I couldn't find Al's equation online, but there was a similar one. How Many Books Is That?: Modeling Amazon Sales Rank – Uncertain Principles Different numbers, but the same form as Al's, with x^(-1.126) being the correct interpretation.
 04-04-2015, 07:13 AM #14 Thinks s/he gets paid by the post   Join Date: Aug 2006 Posts: 2,366 The best way to solve this type of problem is to write the equation in terms of symbols and plug the numbers in at the end. y = A x^z where A=176091 and z = -1.126 x^z = y/A Raise both sides to the 1/z power x = (y/A)^(1/ z) 1/z = -1/1.126 = -0.8881 x = (y/A)^-0.8881 = (A/y)^0.8881 = ((176091)^0.8881)/(y^0.8881) x = 45576/(y^0.8881) which agrees with karluk's result (by not doing it with symbols first, I made an error in my post above ) __________________ __________________ I'd rather be governed by the first one hundred names in the telephone book than the Harvard faculty - William F. Buckley

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