P varies directly as N and inversely as M. If M = 12, P = 9, and N = 8, find N when M = 17 and P = 27.
A
35
B
34
C
36
D
38
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
P varies directly as N and inversely as M
P = \(\frac{\text{k N}}{\text{M}}\)
9 = \(\frac{ 8k}{12}\)
8k = 12 x 9
K = \(\frac{108}{8}\) = 13.5
P = \(\frac{13.5 N}{\text{M}}\)
Find N, when M = 17, P = 27
27 = \(\frac{13.5 N}{17}\)
13.5 N = 27 x 17 = 459
N = \(\frac{459}{13.5\) = 34.
Source: Myschool Past Questions Archive (Record #78182)