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?
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
----------------------
        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.