document.write( "Question 1151041: Question: A motor car is three times as old as its tires were when it was as old as the tires are now. When its tires are as old as the car is now, the car will be a year older than the tires are now. What are the present ages of car and tires?\r
\n" ); document.write( "\n" ); document.write( "Answer:The car is 18 months old the tires are a year old \r
\n" ); document.write( "\n" ); document.write( "What is the math formula for the answer? \n" ); document.write( "

Algebra.Com's Answer #772634 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "Let x be the age of the car (in months), and\r\n" );
document.write( "\r\n" );
document.write( "let y be the age of the tires (in months, again).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When the car was as old as the tires are now ?  --- Obviously, (x-y) months ago.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, according to the first part of the condition\r\n" );
document.write( "\r\n" );
document.write( "    x = 3*(y - (x-y)).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify it:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x = 3*(2y-x)  \r\n" );
document.write( "\r\n" );
document.write( "    x = 6y - 3x\r\n" );
document.write( "\r\n" );
document.write( "    x + 3x = 6y\r\n" );
document.write( "\r\n" );
document.write( "    4x = 6y\r\n" );
document.write( "\r\n" );
document.write( "    2x = 3y.           (1)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When the car's tires will be as old as the car is now ?  ----  In (x-y) months, obviously.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, according to the second part of the condition,\r\n" );
document.write( "\r\n" );
document.write( "    x + (x-y) = y + 12    months.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify it:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    2x - y = y + 12,\r\n" );
document.write( "\r\n" );
document.write( "    2x - 2y = 12.      (2)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From equation (1), substitute 2x = 3y into equation (2), replacing 2x by 3y there.  You will get then\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    3y - 2y = 12,\r\n" );
document.write( "\r\n" );
document.write( "     y      = 12.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus, the tires current age is 12 months.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then from (1),  2x = 3y = 3*12 = 36;  hence,  x = 36/2 = 18.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The car is 18 months old.  The tires are 12 months old.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "There is a bunch of lessons on age word problems \r
\n" ); document.write( "\n" ); document.write( "    - Age problems and their solutions\r
\n" ); document.write( "\n" ); document.write( "    - A fresh formulation of a traditional age problem\r
\n" ); document.write( "\n" ); document.write( "    - Really intricate age word problems (*)\r
\n" ); document.write( "\n" ); document.write( "    - Selected age word problems from the archive\r
\n" ); document.write( "\n" ); document.write( "    - Age problems for mental solution \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solving age problems.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Of these lessons, for the most close problems to yours in this post, is the lesson marked (*) in the list.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Age word problems\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );