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
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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
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
:
