SOLUTION: Hi. I need some help with the following problem. Thanks Use the given information to find the constant of proportionality. S varies jointly as p and q. If p = 3 and q = 7, then

Algebra ->  Equations -> SOLUTION: Hi. I need some help with the following problem. Thanks Use the given information to find the constant of proportionality. S varies jointly as p and q. If p = 3 and q = 7, then      Log On


   

Question 124817: Hi. I need some help with the following problem. Thanks
Use the given information to find the constant of proportionality.
S varies jointly as p and q. If p = 3 and q = 7, then S = -21.
k =
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Saying that S varies jointly as p and q means that S is related to the product of p and q as in:
.
S = k*p*q
.
in which k represents the constant of proportionality.
.
You are given that when p = 3 and q = 7, then S = -21. You can use these values to find the
value of k. Substitute 3 for p and 7 for q and -21 for S to get:
.
-21 = k*3*7
.
Multiply out the right side to get:
.
-21 = k*21
.
Divide both sides by 21 ... the multiplier of k ... to get:
.
-21/21 = k
.
This simplifies to
.
k = -1
.
Now return to the original joint variation equation of:
.
S = k*p*q
.
substitute -1 for k and you have the joint variation equation as being:
.
S = -1*p*q = -pq
.
So that is the answer to this problem ... k = -1 and as additional information you have the
additional knowledge that the equation for S is S = -pq
.
Hope this helps you to understand the problem.