How many of each type of hole are there on the golf course?

3 Responses to “How many of each type of hole are there on the golf course?”

1. wjllope says:

   January 28, 2010 at 7:25 am

   equation1: 3*N3 + 4*N4 + 5*N5 = 74
   equation2: N3 + N4 + N5 = 18
   equation3: 2*N5 = N4

   insert equation 3 into equations 1 and 2, and simplify.
   3*N3 + 4*2*N5 + 5*N5 = 74
   N3 + 2*N5 + N5 = 18

   3*N3 + 13*N5 = 74
   N3 + 3*N5 = 18

   now insert the simplified equation 2 into the simplified equation 1, and simplify further.
   3*(18-3*N5) + 13*N5 = 74
   54 – 9*N5 + 13*N5 = 74
   4*N5 = 20
   -> N5 = 5

   via equation3 -> N4 = 10
   via equation2 -> N3 = 3

   hence, 3 par-3s, 10 par-4s, and 5 par-5s….

   cheers

   EDIT: slowfing…. your matrix has a typo
   3 4 5 74
   0 1 -2 0
   1 1 1 18
   References :
2. Big B says:

   January 28, 2010 at 7:37 am

   3 PAR 3’s, 5 PAR 5’s AND 10 PAR 4’s
   References :
3. Slowfinger says:

   January 28, 2010 at 8:13 am

   You have to solve the system of 3 linear equations:
   Let there’s A par-3 holes, B par-4 holes and C par-5 holes.
   A golfer who shoots par on every hole has a total of 74. That means
   3 A + 4 B + 5 C = 74
   There are twice as many par-4 holes as there are par-5 holes.
   B – 2 C = 0
   There are 18 holes in total:
   A + B + C = 18
   So we have system
   3 A + 4 B + 5 C = 74
   0 A + 1 B – 2 C = 0
   1 A + 1 B + 1 C = 18
   with matrix
   3 4 5 74
   0 1 2 0
   1 1 1 18
   Solutions to this system is (choose any method you like) are:
   A = 3, B = 10, C = 5
   There are 3 par-3 holes, 10 par-4 holes and 5 par-5 holes.
   References :