Question 865382


"m varies directly as n and varies inversely as p" means that {{{m=(k*n)/p}}} 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=(k*n)/p}}}. We're also told that "m=9 when n=3 and p=7". Plug these values into the equation and solve for k. 



{{{m=(k*n)/p}}}



{{{9=(k*3)/7}}}



{{{9*7=k*3}}}



{{{63=3k}}}



{{{3k=63}}}



{{{k=63/3}}}



{{{k=21}}}



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Since {{{k=21}}}, we go from {{{m=(k*n)/p}}} to {{{m=(21n)/p}}} (replace k with 21, since k = 21)



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



{{{m=(21n)/p}}}



{{{m=(21*5)/18}}}



{{{m=105/18}}}



{{{m=35/6}}} <font color="red"><--- This is the answer as a fraction</font>



{{{m=5.83333}}} <font color="blue"><--- This is the answer as a decimal</font> (use a calculator. This result will be approximate)