document.write( "Question 122250: The average of Alex's, Bonnie's, and Carl's ages is 9. Four years ago Carl was the same age as Alex is now. In three years, Bonnie's age will be two-thirds Alex's age. How old is each now? \n" ); document.write( "
Algebra.Com's Answer #89753 by MaxLiebling(13)\"\" \"About 
You can put this solution on YOUR website!
The average of Alex's (A), Bonnie's (B), and Carl's (C) ages is 9:
\n" ); document.write( "(A+B+C)/3 = 9
\n" ); document.write( "-> A+B+C =27; (1)
\n" ); document.write( "Four years ago Carl was (C-4) the same age as Alex is now:
\n" ); document.write( "C-4 = A
\n" ); document.write( "-> C = A+4; (2)
\n" ); document.write( "In three years, Bonnie's age will be two-thirds Alex's age:
\n" ); document.write( "In three years B+3, A+3
\n" ); document.write( "B+3 = 2/3 * (A+3)
\n" ); document.write( "-> B = -3 + (2/3)*(A+3)
\n" ); document.write( "-> B = -3 +(2/3)*A + (2/3)*3
\n" ); document.write( "-> B = -3 +(2/3)*A + 2
\n" ); document.write( "-> B = -1 +(2/3)*A; (3)\r
\n" ); document.write( "\n" ); document.write( "Put results (2) and (3) to (1):
\n" ); document.write( "27 = A+B+C = A + [-1+(2/3)*A] + A+4 = A - 1 +(2/3)*A + A + 4 = 2A+(2/3)*A - 1 + 4 = (8/3)*A + 3 = 27
\n" ); document.write( "-> (8/3)*A = 24
\n" ); document.write( "-> 8*A = 72
\n" ); document.write( "-> A = 9
\n" ); document.write( "--------
\n" ); document.write( "Use (2):
\n" ); document.write( "C = A+4 = 9+4 = 13
\n" ); document.write( "------------------
\n" ); document.write( "Use (3):
\n" ); document.write( "B = -1 +(2/3)*A = -1 +(2/3)*9 = -1 + 6 = 5
\n" ); document.write( "... or ... use (1)
\n" ); document.write( "A+B+C =27 ->
\n" ); document.write( "B = 27 - A - C = 27 - 9 - 13 = 18-13 = 5
\n" ); document.write( "B = 5
\n" ); document.write( "-----
\n" ); document.write( "Proof:
\n" ); document.write( "A+B+C = 9+5+13 = 14+13 = 27 ... okey.
\n" ); document.write( "C-4 = 13-4 = 9 = A ... okey.
\n" ); document.write( "B+3 = 5+3 = 8
\n" ); document.write( "2/3 * (A+3) = (2/3) * (9+3) = (2/3) * 12 = 24/3 = 8 = B+3 ... okey.
\n" ); document.write( "
\n" );