Question 278339: Can you help me solve for variation: n varies directly as q, and n=39 when q=3. Find n when q =8.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! n varies directly as q.
n = 39 when q = 3
find n when q = 8
n varies directly as q means that n = k*q
this means that:
39 = k*3
divide both sides of this equation by 3 to get:
k = 13
now that you have the value of k, you can solve for finding n when q = 8
you get:
n = k*q becomes n = 13*8 which becomes n = 104
in a direct variation problem, the ratio between n and q remains the same.
this means that n1 is to q1 as n2 is to q2.
in formula terms, this would be n1/q1 = n2/q2
in your problem, this becomes:
39/3 = 104/8
cross multiply and you get 39*8 = 3*104 which becomes 312 = 312 confirming that the ratio is the same between the 2 numbers of n/q.
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