Gravity Ratios using pronumerals

[yakiland]

Homework Statement

There are two planets called Alpha and Beta.
mass of alpha=M
mass of beta=0.01M
They are distance R apart.

At what distance, expressed in terms of R, from the planet Alpha, along a straight line joining the centres of Alpha and Beta, will the ratio of [force alpha : force beta] on an asteroid be equal to 8100?

Homework Equations

I avoided the use of Newtons universal theory of gravity since there are no actual numbers. i used ratios instead.

The Attempt at a Solution

here goes...

[mass (alpha)/distance (alpha)] / [mass (beta)/distance (beta)]=8100

let x be the distance between alpha and the asteroid.
[M/xR] / [0.01M/(R-xR)]=8100

Simplify:
[1-x/0.01x]=8100

Solve for x:
x=0.012R

but the answer is 0.909R!

Thanks for your help.

 

[yakiland]

sorry, quick correction to the answer to the above question.

the book says the answer is 0.1R.

 

[yakiland]

dont worry, did it