P varies directly as q and s but inversely as t and v. P is 360 when q=5, s=6, t=4, and v=7. Find P when q=30, s=40, t=50, and v=70.

Question

The teacher gave us these equations to use:

 

directly: y=kx

inversely: y=k/x

Answer 1

A function has:
  independent variable(s), usually indicated as x.  These variables change "whenever they want to."
  dependent variable, usually indicated as y.  It depends on the value of the independent variable (x).
  constants, often indicated as A, B, C, m, b, k, ...   They don't change value.
 
The function y = kx has one of each (which is which??).

 

This problem has P,k,q,s,t,v  (which of those are which??).

 

  P = k * ( (q*s) / (t*v) )       (be sure to match this with the problem statement)

 

Note: just like writing (x,y) with the dependent variable last, we write (q,s,t,v,P).

We need one point (q,s,t,v,P) in order to determine the constant k.  The problem gives us (5,6,4,7,360).

      360 = k * ( (5*6) / (4*7) )

       360  = k * (15/28)

       (28/15)360  =  k              (multiply both sides by 21/15)

            k = 336      (they didn't tell us the units)

 

So, what is P at the point (30, 40, 50, 70, P) ??

       P = 336 * ( (30*40) / (50*70) )             (note: I write this way so I can paste into Excel)

       P = 115.2

Answer 2

P = kqs/(tv)

 

Since P = 360 when q = 5, s = 6, t = 4 and v = 7, 

 

360 = k(5)(6)/[(4)(7)]

 

360 = 30k/28

 

k = 336

 

So, P = 336qs/(tv)

 

Therefore, when q = 30, s = 40, t = 50, and v = 70,

 

P = 336(30(40)/[(50)(70)] = 115.2 

Answer 3

The question doesn't specify the nature of relationship, but the above answer is correct now I see it.

So as mentioned in your question:
For direct proportionality,
p=kq
p=ls
 
While for inverse proportionality,
p=m/t
p=n/v

 

I chose k, l, m, and n arbitrarily as constants for the relations.
 
If p=360 when q=5, then, k=360/5 = 72
If p=360 when s=6, then l=360/6 = 60
If p=360 when t=4, then m=360*4= 1440
If p=360 when v=7, then n=360*7 = 2520
 
Now that we have the constants of relationship, we can find p for each value of the of variables.
So,
 
For q=30,  p=kq=72*30=2160
For s=40,   p=ls=60*40=2400
For t=50,  p= m/t = 1440/50 = 28.8
For v=70, p=n/v = 2520/70 = 36