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Math Help - 3X3 system word problem

  1. #1
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    3X3 system word problem

    A certain 18-hole golf course has par-3, par-4 and par-5 holes and there are twice as many par-4 holes as there are par-5 holes. How many holes of each type are there if a golfer has par on every hole for a score of 70?

    All I need is the 3 equations to solve it and I'll be able to do the rest.
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  2. #2
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    Hello, Itsbaxagain!

    A certain 18-hole golf course has par-3, par-4 and par-5 holes.
    There are twice as many par-4 holes as there are par-5 holes.
    How many holes of each type are there if a golfer has par on every hole for a score of 70?
    Let: . \begin{Bmatrix}x &=&\text{no. of par-3 holes} \\ y &=&\text{no. of par-4 holes} \\ z &=&\text{no. of part-5 holes} \end{Bmatrix}

    There are 18 holes on the course: . {\color{blue}x + y + z \:=\:18}

    There are twice as many y's as z's\!: \;\;y \:=\:2z\quad\Rightarrow\quad {\color{blue}y - 2x \:=\:0}

    A golfer made par on every hole for a score of 70: . {\color{blue}3x + 4y + 5z \:=\:70}

    . . . Go for it!

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