SOLUTION: Hello, I'm stuck on this word problem. At the Halloween event there were 335 people in costume. There were 31 fewer vampires than witches and four times as many ghosts as all

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Question 526481: Hello,
I'm stuck on this word problem. At the Halloween event there were 335 people in costume. There were 31 fewer vampires than witches and four times as many ghosts as all of the vampires and witches together. How many ghosts were there?
Thanks for your help.
Answer by stanbon(57962) (Show Source):
You can put this solution on YOUR website!
At the Halloween event there were 335 people in costume. There were 31 fewer vampires than witches and four times as many ghosts as all of the vampires and witches together. How many ghosts were there?
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Equations:
v + w + g = 335
v = w-31
g = 4(v+w)
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Rearrange the equations:
v + w + g = 335
v - w + 0 = -31
4v+4w - g = 0
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I used a matrix method to get:
v = 18
w = 49
g = 268 (# of ghosts)
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Cheers,
Stan H.