SOLUTION: Thanks for your help on this one: On an 18-hole golf course, there are par-3 holes, par-4 holes and par-5 holes. A golfer who shoots par on every hole has a score of 72. The sum of

Question 116992This question is from textbook
: Thanks for your help on this one: On an 18-hole golf course, there are par-3 holes, par-4 holes and par-5 holes. A golfer who shoots par on every hole has a score of 72. The sum of the number of par-3 and the number of par-5 holes is 8. How many of each type of hole are there on the golf course? This question is from textbook

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
On an 18-hole golf course, there are par-3 holes, par-4 holes and par-5 holes. A golfer who shoots par on every hole has a score of 72. The sum of the number of par-3 and the number of par-5 holes is 8. How many of each type of hole are there on the golf course?
Let:
x = no. of par 3 holes
y = no. of par 4 holes
z = no. of par 5 holes:
:
We know:
x + y + z = 18
:
3x + 4y + 5z = 72
:
It says,"The sum of the number of par-3 and the number of par-5 holes is 8."
x + z = 8
or
z = (8-x)
:
In the 1st equation substitute (8-x) for z:
x + y + (8-x) = 18
x - x + y = 18 - 8
y = 10 par 4 holes
:
In the 2nd equation substitute 10 for y and (8-x) for z
3x + 4(10) + 5(8-x) = 72
3x + 40 + 40 - 5x = 72
3x - 5x + 80 = 72
-2x = 72 - 80
-2x = -8
x = -8/-2
x = 4 par 3 holes
Then
8 - 4 = 4 par 5 holes
:
:
Check 4(3) + 10(4) + 4(5) =
12 + 40 + 20 = 72
:

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