Solve $p,q,r,s,t$ for this set of statements Obtained from the UKMT IMK Grey 2014 Q21:
Note that I DO NOT want answers; only hints. 

An antique set of scales is not working properly. If something is lighter than 1000g, the scales
  show the correct weight, otherwise, the scales can show any value greater than 1000g.
  Jenny grows giant fruit and vegetables. She has a pumpkin, a quince, a radish, a swede and a
  turnip whose weights are all less than 1000g and, in grammes, are
  P, Q, R, S and
  T.
  When she weighs them in pairs, the scale shows the following:
  quince and swede: 1200g radish and turnip: 2100g quince and turnip: 800g
  quince and radish: 900g pumpkin and turnip: 700g. Which of the following lists gives the masses in descending order?

So, in this question, I have obtained:
1) $q+s>1000$
2) $r+t>1000$
3) $q+t = 800$
4) $p+t = 700$
5) $q+r = 900$
I added 4) and 5) to get $p+r+q+t=1600$, which gets taken away from 3) to get:
6) $p+r=800$
Also, 1) + 2) is 
7) $q+r+s+t>2000$
I have retrieved these(not necessarily useful) equations/inequalities. I do not know how to get on from here.
 A: Some additional things you can use:


*

*Subtracting (4) from (3) gives you $r - t = 100$, which you can combine with (2) to get some lower bounds on both $r$ and $t$.

*Subtracting (5) from (4) gives you $q - p = 100$.

*You are also given $0 < p, q, r, s, t < 1000$, which you can combine with other information to get tighter bounds (for example, since $q - p = 100$, you can state that $0 < p < 900$ and $100 < q < 1000$).

A: Equations 6) and 7) seems to be useless (contains less informations than previous equations)


*

*Solve the system of equations 3), 4) and 5) - you will obtain the solution depending on parameter $t=\tau$

 $\begin{cases}t=\tau\\ q=800-\tau \\ p=700-\tau\\ r=100+\tau \end{cases}$  


*From 2) you obtain the lower boundary for $\tau$

 $\tau > 450$


*From 1) you obtain another parameter ($s=\sigma$) and it's relation with $\tau$:

 $\sigma > 200 +\tau$ 


*Now it is easy to see two groups of inequalities:

 $s>200+\tau > 100+\tau=r>\tau=t$ and $q=800-\tau>700-\tau = p$, so $\,\,s>r>t$ and $q>p$


*Result of second step compared with the result of step 4. gives us connection between these groups:

 $t=\tau>450 >350=800-450 >800-\tau =q$

