SOLUTION: Assume that y varies directly as x. Find y when x=54 if y=1/4 when x=3/2

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Question 101788: Assume that y varies directly as x. Find y when x=54 if y=1/4 when x=3/2
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

since x and y are directly proportional, there must be such of number n where y=n%2Ax
+x+%3A+%283%2F2%29+=+y+%3A+%281%2F4%29
then
x%2A%281%2F4%29+=+y%2A%283%2F2%29
+y+=+%281%2F4%29%2Ax%2F%283%2F2%29
y+=+%281%2F4%29%2A%282%2F3%29+%2Ax
y+=%281%2F6%29x+ so, n=1%2F6
if x=54 we have
y=%281%2F6%29%2A54
y+=+9
check:
+x+%3A+%283%2F2%29+=+y+%3A+%281%2F4%29
+54+%3A+%283%2F2%29+=+9%3A+%281%2F4%29
108%3A3+=+36%3A1
36+=+36

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
y varies directly as x.
So, y = kx
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Find y when x=54 if y=1/4 when x=3/2
1/4 = k(3/2)
Multiply both sides by 4 to get:
1 = 6k
k = 1/6
So the general equation is y = (1/6)x
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Now fid y if x = 54
y = (1/6)*54
y = 9
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Cheers,
Stan H.