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

R03.jpg
kadinAsked:
Who is Participating?

[Product update] Infrastructure Analysis Tool is now available with Business Accounts.Learn More

x
I wear a lot of hats...

"The solutions and answers provided on Experts Exchange have been extremely helpful to me over the last few years. I wear a lot of hats - Developer, Database Administrator, Help Desk, etc., so I know a lot of things but not a lot about one thing. Experts Exchange gives me answers from people who do know a lot about one thing, in a easy to use platform." -Todd S.

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

2PS=256rpm =>

PS=128rpm
X=128rpm
Paul SauvéRetiredCommented:

1. one pulley is twice as large in diameter as a second pulley

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!
kadinAuthor 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.
JavaScript Best Practices

Save hours in development time and avoid common mistakes by learning the best practices to use for JavaScript.

Paul SauvéRetiredCommented:
(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

Experts Exchange Solution brought to you by

Your issues matter to us.

Facing a tech roadblock? Get the help and guidance you need from experienced professionals who care. Ask your question anytime, anywhere, with no hassle.

Start your 7-day free trial
aburrCommented:
"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
kadinAuthor Commented:
Thank you all for helping me learn how to put this together. Little by little I will learn this.
aburrCommented:
"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
kadinAuthor Commented:
Thanks again. It seems to help to know things like (cir = pi * diam). I think that's from geometry.
It's more than this solution.Get answers and train to solve all your tech problems - anytime, anywhere.Try it for free Edge Out The Competitionfor your dream job with proven skills and certifications.Get started today Stand Outas the employee with proven skills.Start learning today for free Move Your Career Forwardwith certification training in the latest technologies.Start your trial today
Math / Science

From novice to tech pro — start learning today.