Three golfers, Vijay, Ernie, and Phil , during five years had a total of 221 top-10 finishes. Ernie had 13 more top-10 finishes than Phil. Vijay had 16 more top-10 finishes than Phil. Determine the number of top-10 finishes for each golfer.

For this case what you must do first is to define the following variables:

x: number of top-10 finishes for Vijay.

y: number of top-10 finishes for Ernie.

z: number of top-10 finishes for Phil.

We write the following system of equations:

x + y + z = 221

y = 13 + z

x = 16 + z

Solving the system we have:

Step 1:

x + y + z = 221

(13 + z) + (16 + z) + z = 221

3z + 29 = 221

z = (221-29) / (3)

z = 64

Step 2:

y = 13 + z

y = 13 + 64

y = 77

Step 3:

x = 16 + z

x = 16 + 64

x = 80

Answer:

the number of top-10 finishes for each golfer is:

Vijay: 80

Ernie: 77

Phil 64