document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #323590 by karaoz(32) $\"\"$ $\"About$

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T = age of Tim
\n" ); document.write( "C = age of Tim's coach

\n" ); document.write( "Translation of the fact described by the first sentence in the problem statement:
\n" ); document.write( "(C - 3) = 2(T - 3).

\n" ); document.write( "Translation of the fact described by the second sentence in the problem statement:
\n" ); document.write( "C = T + 10.

\n" ); document.write( "Translation of the third sentence in the problem statement:
\n" ); document.write( "T = ?

\n" ); document.write( "Solve the system of equations to find T:

\n" ); document.write( "(C - 3) = 2(T - 3)
\n" ); document.write( "C = T + 10

\n" ); document.write( "First, simplify the first equation:
\n" ); document.write( "C - 3 = 2T - 6
\n" ); document.write( "C - 2T = -3
\n" ); document.write( "Multiply the equation by -1 to get a nicer form of the equation:
\n" ); document.write( "2T - C = 3.

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

\n" ); document.write( "Simplify:
\n" ); document.write( "2T - T - 10 = 3
\n" ); document.write( "T - 10 = 3

\n" ); document.write( "Add 10 to the both sides of the equation (purpose is to isolate T on one side):
\n" ); document.write( "T - 10 + 10 = 3 + 10
\n" ); document.write( "Simplify:
\n" ); document.write( "T = 13

\n" ); document.write( "Answer: Tim is 13 years old.\r
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