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
 
 the number of top-10 finishes for each golfer is:
 Vijay: 80
 Ernie: 77
 Phil 64

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