St andrews golf course in st andrews scotland is one of the oldest courses in the world. it is an 18-hole course that consists of par-3 holes, par-4 holes and par-5 holes. a golfer who shoots par at the old course at st andrews has a total of 72 strokes for the entire course. there are seven times as many par-4 holes as par- 5 holes,and the sum of the numbers of par-3 and par-5 holes is four.find the numbers of par-3, par-4 and par-5 holes in the course?
let x represent the par 3
let x represent the par 3
y represent the pr 4
z represent the par 5
18-hole course that consists of par-3 holes, par-4 holes and par-5 holes.
so x + y + z = 18 ..............(1)
seven times as many par -4 holes as par -5 holes
so y = 7z .............(2)
sum of the number of par-3 and par 5 holes is four
so x + z = 4
subtract z both side we get
x = 4- z ................(3)
put the value of x and y in equation first we get
4-z + 7z + z = 18
4 + 7z = 18
7z = 18- 4
z = 14/7
z = 2
put the value of z in equation second and third we get
y = 7z
= 7* 2
= 14
and x = 4-z
=4- 2
= 2
Answer is x= 2 , y = 14 and z = 2
