precalculus
posted by snow .
st andrews golf course in st andrews scotland is one of the oldest courses in the world. it is an 18hole course that consists of par3 holes, par4 holes and par5 holes. a golfer who shoots par at the old course at st andrews has a total of 72 strokes for the entire course. there are seven times as many par4 holes as par 5 holes,and the sum of the numbers of par3 and par5 holes is four.find the numbers of par3, par4 and par5 holes in the course.

Let's set up some variables to keep track of the various items of interest.
a = # par3 holes
b = # par4 holes
c = # par5 holes
We are told:
a+b+c=18 holes
b = 7c
a+c = 4
3a+4b+5c = 72 strokes needed to finish course
3(4c) + 4(7c) + 5c = 72
123c + 28c + 5c = 72
30c = 60
c=2
b=14
a=2
And we didn't even need the fact that a+b+c=18, but it works out just fine.
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