# 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

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Mixtures -> 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      Log On

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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 Answer by ankor@dixie-net.com(15652)   (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. 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 :