Joint variation (show work)

1. a varies jointly as b and c. One set of values is a=86.4 when b=9 and c=12. Find a when b=20 and c=6.5

a = kbc

86.4 = k (9)(12)

86.4 = k (108)

86.4 / 108 = k  =  4/5

So

a = (4/5) (20) (6.5)

a =   16 * 6.5

a = 104

2. m varies jointly as n and p. One set of vales is m=60 when n=4 and p=5. Find m when n=12 and p=2

m =  knp

60 = k (4)(5)

60 = 20k

60/20 = k = 3

So

m = 3 (12) (2) 

m = 72