# SOLUTION: 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 holes and th

Algebra ->  Algebra  -> Systems-of-equations -> SOLUTION: 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 holes and th      Log On

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 Question 145091: 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 holes and the number of par -5 holes is 8. How many of each type of hole are there on the golf course? Answer by stanbon(57967)   (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. # of holes equation: t + f + v = 18 ------------------ A golfer who shoots par on every hole has a score of 72. par equation: 3t + 4f + 5v = 72 ------------------ The sum of the number of par-3 holes and the number of par -5 holes is 8. Added info equation: t + v = 8 ---------------------------------- How many of each type of hole are there on the golf course? -------------- You have three equations with three variables: t + f + v = 18 t + 0 + v = 8 3t+4f +5v = 72 ------------------ Subtract 2nd equation from 1st to get: 0 + f + 0 = 10 (so # of par 4 holes is 10) t + 0 + v = 8 3t+4f +5v = 72 ---------------------- Subtract 3 times the 2nd from the 3rd to get: 0 + f + 0 = 10 t + 0 + v = 8 0+ 4f +2v = 48 ------------------- Since f = 10, substitute into the 3rd equation and solve for v: 4*10 + 2v = 48 2v = 8 v = 4 (so # of par five holes is 4) ------------------------- Since t + f + v = 18 t + 10 + 4 = 18 t = 4 ================ t = 4 f = 10 v = 4 =========== Cheers, Stan H.