SOLUTION: If m varies directly as n and varies inversely as p, and m=9 when n=3 and p=7, find m when n=5 and p=18.

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Question 865382: If m varies directly as n and varies inversely as p, and m=9 when n=3 and p=7, find m when n=5 and p=18.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

"m varies directly as n and varies inversely as p" means that m=%28k%2An%29%2Fp for some fixed number k (k is a constant).


We are told that "m varies directly as n and varies inversely as p" which means m=%28k%2An%29%2Fp. We're also told that "m=9 when n=3 and p=7". Plug these values into the equation and solve for k.


m=%28k%2An%29%2Fp


9=%28k%2A3%29%2F7


9%2A7=k%2A3


63=3k


3k=63


k=63%2F3


k=21


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Since k=21, we go from m=%28k%2An%29%2Fp to m=%2821n%29%2Fp (replace k with 21, since k = 21)


Now we plug in n = 5 and p = 18 into that last equation to find m


m=%2821n%29%2Fp


m=%2821%2A5%29%2F18


m=105%2F18


m=35%2F6 <--- This is the answer as a fraction


m=5.83333 <--- This is the answer as a decimal (use a calculator. This result will be approximate)