Need Algebra Help

[TromboneAl]

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.

 

[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 .... ?

 

[mystang52]

y=176091[x(-1.126)]
y/176091= x(-1.126)
(y/176091)/-1.126=x

 

[Elbata]

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.

 

[Peter]

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 ....

 

[Elbata]

I see what you're saying Peter, I was just having fun using math that I've learned from Khan Academy.

 

[FIRE'd@51]

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.

 

[mystang52]

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.

 

[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.

 

[karluk]

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)

 

[karluk]

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.

 

[steelyman]

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.

 

[Animorph]

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.

 

[FIRE'd@51]

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 )