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

Question 126566: 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 on every hle for a score of 70?
Answer by marcsam823(57) (Show Source): You can put this solution on YOUR website!
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

RELATED QUESTIONS
A certain 18-hole golf course has par-3, par-4, and par-5 holes, and there are twice as... (answered by stanbon)

On an 18-hole golf course, there are par-3 holes, par-4 holes, and par-5 holes. A golfer (answered by mathtutor777)

(I need help with this question, please?) On an 18-hole golf course, there are par-3... (answered by richwmiller)

On an 18-hole golf course, there are par-3 holes, par-4 holes, and par-5 holes. A golfer... (answered by stanbon)

Thanks for your help on this one: On an 18-hole golf course, there are par-3 holes, par-4 (answered by ankor@dixie-net.com)

please help me I never took this until now and is like I am learning a foreign language.... (answered by rothauserc)

jeff played 18 holes on sat. on each of 6 holes he was 1 under par, on each of 4 holes he (answered by checkley71)

PLEASE HELP!!!!!You are playing 3-hole golf. On the first hole you score 1 under par, on... (answered by Alwayscheerful)

You are playing 3-hole golf. On the first hole you score 1 under par, on the second hole... (answered by Alwayscheerful)