SOLUTION: I have problems with word problems. I can't seem to figure this out. Please help me solve this equation: If a wagon wheel had 10 more spokes, the angle between spokes would decrea

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Question 154289: I have problems with word problems. I can't seem to figure this out.
Please help me solve this equation: If a wagon wheel had 10 more spokes, the angle between spokes would decrease by 6 degrees. How many spokes does the wheel have?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If a wagon wheel had 10 more spokes, the angle between spokes would decrease by 6 degrees. How many spokes does the wheel have?
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Let the number of spokes be "x"; then there are x equal central angles
and each is 360/x degrees.
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If there were 10 more spokes there would be "x+10" angles;
each would be 360/(x+10) degrees.
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EQUATION:
old angle size - new angle size = 6 degrees
360/x - 360/(x+10) = 6
1/x - 1/(x+10) = 1/60
60(x+10) - 60x = x(x+10)
600 = x^2+10x
x^2+10x-600 = 0
(x+30)(x-20) = 0
Positive solution:
x = 20 (original number of spokes)
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Cheers,
Stan H.