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pre-calculus

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st andrews golf course in st andrews scotland is one of the oldest courses in the world. it is an 18-hole course that consists of par-3 holes, par-4 holes and par-5 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 par-4 holes as par- 5 holes,and the sum of the numbers of par-3 and par-5 holes is four.find the numbers of par-3, par-4 and par-5 holes in the course.

  • pre-calculus - ,

    Let's set up some variables to keep track of the various items of interest.

    a = # par-3 holes
    b = # par-4 holes
    c = # par-5 holes

    We are told:
    a+b+c=18 holes
    b = 7c
    a+c = 4
    3a+4b+5c = 72 strokes needed to finish course

    3(4-c) + 4(7c) + 5c = 72
    12-3c + 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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