SOLUTION: find the value of m if e/1 = f/2 = g/3 = (5e - 6f -2g)/m

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Question 1159466: find the value of m if
e/1 = f/2 = g/3 = (5e - 6f -2g)/m
Found 3 solutions by AnlytcPhil, Edwin McCravy, greenestamps:
Answer by AnlytcPhil(1806) About Me  (Show Source):
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Question 1159466

e%2F1+=+f%2F2+=+g%2F3+=+%285e+-+6f-2g%29%2Fm

e%2F1=f%2F2

Cross multiply:

2e=f

f=2e

-------

e%2F1=g%2F3

Cross multiply:

3e=g

g=3e

-------

Substitute 2e for f and 3e for g in

g%2F3+=+%285e+-+6f-2g%29%2Fm

%283e%5E%22%22%29%2F3%5E%22%22+=+%285e+-+6%282e%29-2%283e%29%5E%22%22%29%2Fm%5E%22%22

%28cross%283%29e%29%2Fcross%283%29+=+%285e+-+12e-6e%29%2Fm

e+=+%285e+-+12e-6e%29%2Fm

e+=+%28-7e-6e%29%2Fm

Multiply both sides by m:

em+=+-13e

Divide both sides by e

em%2F%28e%29+=+-13e%2Fe

cross%28e%29m%2Fcross%28e%29+=+-13cross%28e%29%2F%28cross%28e%29%29

m+=+-13

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The given condition

e%2F1+=+f%2F2+=+g%2F3

is satisfied by letting e=x, f=2x, and g=3x; each expression is then equal to x. So then we want the expression

%285e-6f-2g%29%2Fm

to be equal to x also.

%285%28x%29-6%282x%29-2%283x%29%29%2Fm+=+x
-13x%2Fm+=+x
m+=+-13