document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159094>Question 159094</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When John is as old as his father is now, his sister will be twice as old as she is now, and the age of his father will be twice the age john will be when his sister is as old as his father is now.<BR>\n" );
document.write( "The total age of the three is a century.<BR>\n" );
document.write( "How old is everyone now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117260 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=117260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> took a while but i think i have the answer.<BR>\n" );
document.write( "let S = sister's age now.<BR>\n" );
document.write( "let J = john's age now.<BR>\n" );
document.write( "let F = father's age now.<BR>\n" );
document.write( "total age of the three is 100 so S + J + F = 100 (equation 1)*****<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "first part of the problem states that when john is as old as his father is now, his sister will be twice as old as she is now.<BR>\n" );
document.write( "let when that happens be in A years.<BR>\n" );
document.write( "J + A = F (equation 2)*****<BR>\n" );
document.write( "S + A = 2*S (equation 3)*****<BR>\n" );
document.write( "subtracting equation 3 from equation 2 to remove the A, we get<BR>\n" );
document.write( "J-S = F-2*S<BR>\n" );
document.write( "adding 2*S to both sides of the equation, we get<BR>\n" );
document.write( "J+S = F<BR>\n" );
document.write( "subtracting J from both sides of the equation, we get<BR>\n" );
document.write( "S = F-J<BR>\n" );
document.write( "substituting in equation 1 above, we get<BR>\n" );
document.write( "S + J + F = F - J + J + F = 100<BR>\n" );
document.write( "the J cancels out and we are left with 2*F = 100<BR>\n" );
document.write( "dividing both sides of the equation by 100, we get<BR>\n" );
document.write( "F = 50 (equation 4)*****<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "second part of the problem states that the age of his father will be twice the age john will be when his sister is as old as his father is now.<BR>\n" );
document.write( "let B = the number of years in which that will happen.<BR>\n" );
document.write( "then,<BR>\n" );
document.write( "F + B = 2*(J+B) = 2*J + 2*B (equation 5)*****<BR>\n" );
document.write( "S + B = F (equation 6)*****<BR>\n" );
document.write( "solving for F in equation 5, we get<BR>\n" );
document.write( "F + B = 2*J + 2*B<BR>\n" );
document.write( "F = 2*J + 2*B - B<BR>\n" );
document.write( "F = 2*J + B<BR>\n" );
document.write( "since equation 6 also equals F we can make 2*J + B = S + B<BR>\n" );
document.write( "subtracting B from both sides of this equation, we get<BR>\n" );
document.write( "2*J = S<BR>\n" );
document.write( "which is the same as<BR>\n" );
document.write( "S = 2*J (equation 7)*****<BR>\n" );
document.write( "since equation 1 states that F + S + J = 100 and equation 4 states that F = 50 and equation 7 states that S = 2*J, equation 1 becomes<BR>\n" );
document.write( "50 + 2*J + J = 100<BR>\n" );
document.write( "subtracting 50 from both sides and adding the J's together, we get<BR>\n" );
document.write( "3*J = 50<BR>\n" );
document.write( "J = 50/3 (equation 8)*****<BR>\n" );
document.write( "equation 7 states that S = 2*J, so S must be 100/3.<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "we now have 3 ages and need to test to see if they're accurate.<BR>\n" );
document.write( "we have<BR>\n" );
document.write( "F = 50<BR>\n" );
document.write( "J = 50/3<BR>\n" );
document.write( "S = 100/3<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "first part of the problem states that when john is as old as his father is now, his sister will be twice as old as she is now.<BR>\n" );
document.write( "that led to equations 2 and 3.<BR>\n" );
document.write( "since john's age is 50/3 and his father's age is 50, the first part of the first part of the problem can be solved for A.<BR>\n" );
document.write( "50/3 + A = 50<BR>\n" );
document.write( "multiplying both sides of the equation by 3, we get<BR>\n" );
document.write( "50 + 3*A = 150<BR>\n" );
document.write( "subtracting 50 from both sides of the equation, we get<BR>\n" );
document.write( "3*A = 100<BR>\n" );
document.write( "A = 100/3<BR>\n" );
document.write( "so john will be as old as his father is now in 100/3 years.<BR>\n" );
document.write( "substituting in the original equation, we get<BR>\n" );
document.write( "50/3 + 100/3 = 50<BR>\n" );
document.write( "150/3 = 50<BR>\n" );
document.write( "50 = 50 so first part of the first part of the problem checks out.<BR>\n" );
document.write( "second part of the first part of the problem states that in A years his sister will be twice as old as she is now.<BR>\n" );
document.write( "if A = 100/3 and his sister is 100/3 years old now, then in 100/3 years his sister will be 200/3 years old which is twice as old as she is now.<BR>\n" );
document.write( "second part of the first part of the problem checks out.<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "second part of the problem states that the age of his father will be twice the age john will be when his sister is as old as his father is now.<BR>\n" );
document.write( "let B equal the number of years when that happens.<BR>\n" );
document.write( "first part of the second part of the problem states that in B years, father will be twice as old as john will be then.<BR>\n" );
document.write( "equation for this was F+B = 2*J+2*B (equation 5)<BR>\n" );
document.write( "since we know that F = 50 and J = 50/3, this equation becomes<BR>\n" );
document.write( "50 + B = 2*(50/3) + 2*B<BR>\n" );
document.write( "subtracting B from both sides of the equation, we get<BR>\n" );
document.write( "50 = 2*(50/3) + B<BR>\n" );
document.write( "subtracting 2*(50/3) from both sides of the equation, we get<BR>\n" );
document.write( "50 - 2*(50/3) = B<BR>\n" );
document.write( "multiplying both sides of the equation by 3, we get<BR>\n" );
document.write( "150 - 2*50 = 3*B<BR>\n" );
document.write( "50 = 3*B<BR>\n" );
document.write( "B = 50/3<BR>\n" );
document.write( "so in 50/3 years, john's father will be twice as old as john is then.<BR>\n" );
document.write( "substituting for B in equation 5, we get<BR>\n" );
document.write( "50 + 50/3 = 2*(50/3) + 2*(50/3)<BR>\n" );
document.write( "multiplying both sides of the equation by 3, we get<BR>\n" );
document.write( "150 + 50 = 2*50 + 2*50<BR>\n" );
document.write( "200 = 100 + 100<BR>\n" );
document.write( "200 = 200<BR>\n" );
document.write( "so first part of the second part of the problem checks out.<BR>\n" );
document.write( "second part of the second part of the problem states that in B years, sister will be as old as her father is now.<BR>\n" );
document.write( "equation for this is S + B = F<BR>\n" );
document.write( "substituting for known values of S and B and F, we get<BR>\n" );
document.write( "100/3 + 50/3 = 50<BR>\n" );
document.write( "150/3 = 50<BR>\n" );
document.write( "50 = 50<BR>\n" );
document.write( "second part of the second part of the problem checks out.<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "answer to the problem is<BR>\n" );
document.write( "Father = 50 years old now.<BR>\n" );
document.write( "Sister = 100/3 = 33 and 1/3 years old now.<BR>\n" );
document.write( "John = 50/3 = 16 and 2/3 years old now.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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