Algebra (probably easy) problem

[Spirochete]

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.

 

[Mark44]

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.

 

[Spirochete]

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?

 

[NoMoreExams]

When you have equations that share variables, you can always do that setup to eliminate the common variable.

 

[Spirochete]

Yes but you couldn't give a numerical value for just R+T, in this case you'd be left with 25P/9

 

[Mark44]

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.

 

[NoMoreExams]

You have 2 equations and 3 unknowns. Chances are, you will have a free variable.

 

[Spirochete]

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.