Question 145091: On an 18-hole golf course, there are par-3 holes, par-4 holes, and par-5 holes. A golfer who shoots par on every hole has a score of 72. the sum of the number of par-3 holes and the number of par -5 holes is 8. How many of each type of hole are there on the golf course?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! On an 18-hole golf course, there are par-3 holes, par-4 holes, and par-5 holes.
# of holes equation: t + f + v = 18
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A golfer who shoots par on every hole has a score of 72.
par equation: 3t + 4f + 5v = 72
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The sum of the number of par-3 holes and the number of par -5 holes is 8.
Added info equation: t + v = 8
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How many of each type of hole are there on the golf course?
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You have three equations with three variables:
t + f + v = 18
t + 0 + v = 8
3t+4f +5v = 72
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Subtract 2nd equation from 1st to get:
0 + f + 0 = 10 (so # of par 4 holes is 10)
t + 0 + v = 8
3t+4f +5v = 72
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Subtract 3 times the 2nd from the 3rd to get:
0 + f + 0 = 10
t + 0 + v = 8
0+ 4f +2v = 48
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Since f = 10, substitute into the 3rd equation and solve for v:
4*10 + 2v = 48
2v = 8
v = 4 (so # of par five holes is 4)
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Since t + f + v = 18
t + 10 + 4 = 18
t = 4
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t = 4
f = 10
v = 4
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Cheers,
Stan H.
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