Question

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.

Answer 1

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