What is the ratio of t to r in a set of equations involving p, q, r, s, and t?

[bluepillow]

Hey guys, I joined after struggling with a few problems for the past two days. I feel as if the answers are blantanly obvious and I'm just missing the simplest and most important bit(s).

Homework Statement

From the set of equations:
p=3q
pr=qs
(1/2)pr² + (1/2)qs² = (1/2)qt²

involving the unknowns p, q, r, s, and t, find the value of the ratio t to r.

Homework Equations

above

The Attempt at a Solution

The first thing I did was rearrange the top two equations so I can eliminate certain variables from the 3rd equation.
My possible rearrangements are:
p=3q
p=(qs)/r
q=p/3
q=(pr)/s
r=(qs)/p
s=(pr)/q

After a few trial and error replacements I keep getting complicated equations that are going to take a while to type out. Can someone give me a nudge in the right direction? I can't even wrap my head around this.

Also, how can I make this text actually look like an equation like I've seen in other posts? I'll edit it if someone can tell me how to change it, and I'll add the complicated mess I end up with in the end.

 

[JaWiB]

Well, you want to solve the last equation for t/r so see if you can get close to having no t's and r's on the other side and then look for some obvious substitutions to get rid of the t's and r's that are left. I don't know if that helps or not

As for putting equations in your posts, use Latex ([noparse][/noparse] tags--look at the sigma button that says "Show/Hide Latex Reference")

 

[bluepillow]

Thanks for your help. Can someone verify that this looks alright so far? Thanks lots.

\frac{1}{2}pr²+\frac{1}{2}qs²=\frac{1}{2}qt²

\frac{1}{2}pr²=\frac{1}{2}qt²-\frac{1}{2}qs²

\frac{(pr ^2)}{2}= \frac{(qt ^2 -qs ^2 )}{2}

2(pr²) = 2(qt²-qs²)


pr² = qt²-qs²

p = \frac{qt ^2-qs^2}{r^2}

p+qs² = \frac{qt ^2}{r^2}

\frac{p+qs^2}{q} = \frac{t^2}{r^2}

 

[Redbelly98]

bluepillow, welcome to PF

It might be easier to define t/r be another variable, say "a":

a = t/r

then you can sub t = a*r in your last equation (EDIT: I mean the last equation in post #1). Work on eliminating everything till you're just left with one equation for "a".

Also, how can I make this text actually look like an equation like I've seen in other posts? I'll edit it if someone can tell me how to change it, and I'll add the complicated mess I end up with in the end.

For simple equations, you can copy-and-paste the symbols from here:
https://www.physicsforums.com/blog.php?b=347

For the LaTex stuff, the ∑ button shows up in "Advanced" edit mode. There's also info here:
https://www.physicsforums.com/misc/howtolatex.pdf
Be ready for some weird stuff to happen occasionally with LaTex. Sometimes, your edits will not show up right away, and you'll have to refresh the browser window to see them. And if you have a lot of LaTex equations in a single post, it can take awhile to load because an image file must be generated for each LaTex equation.

If you do a forum-wide search on LaTex or Tex, you'll find more info.

 

[bluepillow]

Great! Thank you, I'll try and work on this in the morning.