How many of each type of hole are there on the golf course?
How many of each type of hole are there on the golf course?
On a 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 total of 74. There are twice as many par-4 holes as there are par-5 holes. How many of each type of hole are there on the golf course?
How many par-3 holes are there?
How many par-4 holes are there?
How many par-5 holes are there?
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3 Responses
2.1.2010
Best Answer – Chosen by Voters equation1: 3*N3 + 4*N4 + 5*N5 = 74equation2: N3 + N4 + N5 = 18equation3: 2*N5 = N4insert equation 3 into equations 1 and 2, and simplify.3*N3 + 4*2*N5 + 5*N5 = 74N3 + 2*N5 + N5 = 183*N3 + 13*N5 = 74N3 + 3*N5 = 18now insert the simplified equation 2 into the simplified equation 1, and simplify further.3*(18-3*N5) + 13*N5 = 7454 – 9*N5 + 13*N5 = 744*N5 = 20-> N5 = 5via equation3 -> N4 = 10via equation2 -> N3 = 3hence, 3 par-3s, 10 par-4s, and 5 par-5s….cheersEDIT: slowfing…. your matrix has a typo3 4 5 740 1 -2 01 1 1 18
2.1.2010
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 means3 A + 4 B + 5 C = 74There are twice as many par-4 holes as there are par-5 holes.B – 2 C = 0There are 18 holes in total:A + B + C = 18So we have system3 A + 4 B + 5 C = 740 A + 1 B – 2 C = 01 A + 1 B + 1 C = 18with matrix3 4 5 740 1 2 01 1 1 18Solutions 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.
2.1.2010
3 PAR 3's, 5 PAR 5's AND 10 PAR 4's