SOLUTION: A certain 18 hole golf course has par-3 par-4 and par-5 hole and there are twice as many par-4 holes as there are par-5. How many holes of each type are there if a golfer has par o

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Let x = number of par-3 holes
Let y = number of par-4 holes
Let z = number of par-5 holes
Let (total number of holes on the course)
Let 3x = total number of strokes for par-3 holes
Let 4y = total number of strokes for par-4 holes
Let 5z = total number of strokes for par-5 holes
Let (total strokes to par the course)
Let (number of par-4 holes = twice the number of par-5 holes)

1. We'll start by reducing the number of variables from 3 to 2
Equation 1:
Equation 2:
We know that (from above) so let's substitute for y:
Equation 1:


Equation 2:



Now we have two equations with 2 variables each:
Equation 1 is now:
and
Equation 2 is now:
We can solve for z by eliminating the x variable:
Multiply both sides of Equation 1 by -3:


Add this to Equation 2 and solve for z:

+


Solve for x and y:
We know that y = 2z


We also know that x + y + z = 18



The golf course has 6 par-3 holes, 8 par-4 holes and 4 par-5 holes
Check:
Let's test these results with the original equation 2:




This checks. Our answers are correct.
18 + 32 + 20 = 70