P varies partly as q and partly as the square of R

Question

When p =6,q=8,R=4 and when p=10,q=12,R=5
Find the relationship connecting p,q and R

Answer 1

"P varies partly as q and partly as the square of R"
-----> P = kq + cR^2 , where k and c are constants
given: p=6,q=8, R=4 , then....
6 = 8k + 16c or 3 = 4k + 8c **

given: p=10, q=12, R=5, then ....
10 = 12k + 25c ***

multiply ** by 3 to get
9 = 12k + 24c , we also have 10 = 12k + 25c
subtract those two ....
1 = 1c
c = 1
sub into 3 = 4k + 8c
3 = 4k + 8
k = -5/4

P = -5/4 q + R^2