Algebra: turning word problem into equation

I think the final equation should end up looking like this, for example: (1870)(4.0)=(680)(p)  Solve for the unknown (p). However the question I am stuck on has three unknowns. How do I turn this into an equation? Thanks.

Here is what I have so far: PS=Pulley Small; PL=Pulley Large

PL*256=PS*X  This is how the final equation looks on the other problems.

2PS=PL
PL=256rpm
X=PSrpm

Solve for PS:
2PS*256=PS*X
-PS           -PS
PS*256=X
PS/256=X/256
PS=X/256

Solve for PL:
2PS=PL
2*(X/256)=PL

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Sr. System AnalystCommented:
2PS=PL
PL=256rpm
X=PSrpm

2PS=256rpm =>

PS=128rpm
X=128rpm
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RetiredCommented:

2. the circumference of a circle is pi * diameter

The simple answer is that, since the diameter the first is twice that of the second pulley, one revolution of the larger pulley will cause two revolutions of the smaller one!
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Author Commented:
The simple answer is that, since the diameter the first is twice that of the second pulley, one revolution of the larger pulley will cause two revolutions of the smaller one!

I that's true then the smaller pulley should be 512rpm. I unfortunately do not have the answer in the back of the book to this question.

HainKurt: Is your answer almost correct? Thanks for your response.
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RetiredCommented:
(diam PS) (rpm PS) = (diam PL) (rpm PL)

(1) (rpm PS) = (2) (256) (since PL is twice the diameter AND twice the circumference of PS)

rpm SP = 512

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Commented:
"I that's true then the smaller pulley should be 512rpm"
you so not need an answer it the back of the book. You do not need algebra.
paulsauve:is correct and he has the correct method of solution.
Just think about it. If you peal the circumference of the two pulleys, what is the relationship? the PL has twice the length of PS. so when it goes around the PS goes twice, ie the rpm is twice.
If you want algebra
consider the circumference       PL*pi = x*PS*pi
x = PL/PS = 2      therefore 512 RPM

"2PS=256rpm =>

PS=128rpm
X=128rpm"       this is backwards
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Author Commented:
Thank you all for helping me learn how to put this together. Little by little I will learn this.
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Commented:
"final equation should end up looking like this, for example: (1870)(4.0)=(680)(p) "
-
The goal of algebra is NOT to make one equation look like another. It is to use the rules of algebra to solve the equation.

"However the question I am stuck on has three unknowns"

What are your three?
PS, PL, RPM of PS
What is known?    RPM of PL          The ratio PL/PS   (=2)
what else do you know?      eq of circle       cir = pi * diam
In one minute PL lays down 256 * pi * PL worth of rope
in one minute PS lays down x * pi * PS worth of rope            both these lengths are the same thus
x * pi * PS = 256 * pi * PL
or
x = 256 * PL/PS               but PL/PS = 2                    so
x = 256 * 2          which is 512 as paulsauve: said
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Author Commented:
Thanks again. It seems to help to know things like (cir = pi * diam). I think that's from geometry.
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