Question 80322: 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 total of 70. There are twice as many par-4 holes as there are par-five holes. How many of each type of hole are there on the golf course? How many par-3 holes are there? []
Answer by mathtutor777(6)   (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 total of 70. There are twice as many par-4 holes as there are par-five holes. How many of each type of hole are there on the golf course? How many par-3 holes are there?
Set up 2 equations like this:
x = number of par 3 holes
y = number of par 4 holes
z = number of par 5 holes
x + y + z = 18
3x + 4y + 5z = 70 (the golfer's score)
Now, multiply the top equation by -3 (you'll see why)You get -3x -3y -3z = -54
Add this to the other equation:
-3x - 3y - 3z = -54
3x + 4y + 5z = 70
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y + 2z = 16 See? We got rid of x!
Now, save this last equation without the x; we'll use it in a minute.
The problem says there are twice as many par 4 holes as par 5. This means
y = 2z Substitute 2z for y above and get y + y = 16. So y = 8. You can use y = 8 to substitute into the other equations to solve for the other variables.
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