SOLUTION: When Tim started football 3 years ago, his coach was twice his age. Currently, Tim's coach is 10 years older than him. How old is Tim now?

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Question 471908: When Tim started football 3 years ago, his coach was twice his age. Currently, Tim's coach is 10 years older than him. How old is Tim now?
Answer by karaoz(32) About Me  (Show Source):
You can put this solution on YOUR website!
T = age of Tim
C = age of Tim's coach

Translation of the fact described by the first sentence in the problem statement:
(C - 3) = 2(T - 3).

Translation of the fact described by the second sentence in the problem statement:
C = T + 10.

Translation of the third sentence in the problem statement:
T = ?

Solve the system of equations to find T:

(C - 3) = 2(T - 3)
C = T + 10

First, simplify the first equation:
C - 3 = 2T - 6
C - 2T = -3
Multiply the equation by -1 to get a nicer form of the equation:
2T - C = 3.

Substitute the expression for C from the second equation into the the last form of the first equation:
2T - (T + 10) = 3,
and solve for T.

Simplify:
2T - T - 10 = 3
T - 10 = 3

Add 10 to the both sides of the equation (purpose is to isolate T on one side):
T - 10 + 10 = 3 + 10
Simplify:
T = 13

Answer: Tim is 13 years old.