Question 471908
T = age of Tim
C = age of Tim's coach<br>
Translation of the fact described by the first sentence in the problem statement:
(C - 3) = 2(T - 3).<br>
Translation of the fact described by the second sentence in the problem statement:
C = T + 10.<br>
Translation of the third sentence in the problem statement:
T = ?<br>
Solve the system of equations to find T:<br>
(C - 3) = 2(T - 3)
C = T + 10<br>
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.<br>
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.<br>
Simplify:
2T - T - 10 = 3
T - 10 = 3<br>
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<br>
Answer: Tim is 13 years old.