Algebra (probably easy) problem

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Homework Help Overview

The discussion revolves around a problem involving two equations with three variables, specifically focusing on the relationships between the variables P, R, and T. The original poster is tasked with finding the value of the expression (R+T)/R based on the given ratios P/R=3/5 and P/T=9/10.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss various attempts to manipulate the equations, including adding them together and solving for P. There is a suggestion to solve for R and T individually and substitute those values into the target expression. Some participants express surprise at the potential for cancellation of P.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem. There is recognition that without knowing the value of P, obtaining a numerical value for (R + T)/R is challenging. However, some participants suggest that the specific structure of the equations may allow for a numerical answer due to cancellation.

Contextual Notes

Participants note the constraints of having two equations with three unknowns, leading to the possibility of a free variable. There is an emphasis on the necessity of knowing P to derive numerical values for R and T.

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Homework Statement



There are two equations and 3 variables and I'm asked to solve for the numerical value of a third expression:

We are told that

P/R=3/5

P/T=9/10

The question asks for the value of (R+T)/R

Homework Equations



The correct answer is 5/3 but I have no idea how to get there. This is from a GRE practice test.



The Attempt at a Solution



I tried addin' em together. Also solving for "P" to get rid of it doesn't work right away.
 
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Spirochete said:

Homework Statement



There are two equations and 3 variables and I'm asked to solve for the numerical value of a third expression:

We are told that

P/R=3/5

P/T=9/10

The question asks for the value of (R+T)/R

Homework Equations



The correct answer is 5/3 but I have no idea how to get there. This is from a GRE practice test.



The Attempt at a Solution



I tried addin' em together. Also solving for "P" to get rid of it doesn't work right away.

Try solving the first equation for R and the second for T. Then substitute those values into the expression you need to evaluate.
 
oh I did not see in advance that the P's would cancel out like that and I'd get a number. I never would've thought to do that. Could you explain how you saw that?
 
When you have equations that share variables, you can always do that setup to eliminate the common variable.
 
Yes but you couldn't give a numerical value for just R+T, in this case you'd be left with 25P/9
 
Spirochete said:
Yes but you couldn't give a numerical value for just R+T, in this case you'd be left with 25P/9
This is to be expected. You can't get a numerical value for R unless you know P, and you can't get a numerical value for T unless you know P. Since you don't know P, you are not going to be able to get a numerical value for (R + T)/R.
 
You have 2 equations and 3 unknowns. Chances are, you will have a free variable.
 
Mark44 said:
This is to be expected. You can't get a numerical value for R unless you know P, and you can't get a numerical value for T unless you know P. Since you don't know P, you are not going to be able to get a numerical value for (R + T)/R.

Actually I believe this is a special case where you can get a numerical answer just because the P's happen to cancel.
 

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