document.write( "Question 1183712: 5 years back the ratio of kate and sharon 4:3. In 5 years, the sum of the ages of kate and sharon will be 90. how old is sharon right now? \n" ); document.write( "
Algebra.Com's Answer #814155 by ikleyn(52803)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "5 years back the ratio of kate and sharon 4:3.
\n" ); document.write( "In 5 years, the sum of the ages of Kate and Sharon will be 90.
\n" ); document.write( "How old is Sharon right now?
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "In his post, @josgarithmetic writes equation \r\n" );
document.write( "\r\n" );
document.write( "    \"%2890-x-5%29%2F%28x-5%29\" = \"4%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and states that it can be easily solved.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "I tried to follow his instruction\r\n" );
document.write( "\r\n" );
document.write( "    3*(90-x-5) = 4*(x-5)\r\n" );
document.write( "\r\n" );
document.write( "    270 - 3x - 15 = 4x - 20\r\n" );
document.write( "\r\n" );
document.write( "    270 - 15 + 20 = 4x + 3x\r\n" );
document.write( "\r\n" );
document.write( "         275      = 7x\r\n" );
document.write( "\r\n" );
document.write( "          x       = \"275%2F7\" = 39 \"2%2F7\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice that this value even is not integer.\r\n" );
document.write( "\r\n" );
document.write( "@josgarithmetic does not declare what his unknown  \" x \"  is.\r\n" );
document.write( "\r\n" );
document.write( "But it is clear that  NEITHER Kate age  NOR Sharon age  is  non-integer number in this problem.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    +------------------------------------------------------------------------------------------+\r\n" );
document.write( "    |                 You may ask: WHAT IS THE MATTER ?                                        |\r\n" );
document.write( "    |                                                                                          |\r\n" );
document.write( "    |                                                                                          |\r\n" );
document.write( "    |  The matter is that this @josgarithmetic's setup equation is  I N C O R R E C T.         |\r\n" );
document.write( "    |                                                                                          |                                                                                        |\r\n" );
document.write( "    |    In other words (to make my statement even more clear), it is  W R O N G.              |\r\n" );
document.write( "    +------------------------------------------------------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Unfortunately, tutor @greenestamps MISSED this error and declared the @josgarithmetic's setup as \"fine\",  instead.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        THEREFORE, I came to prevent this huge mistake considering the WRONG setup as a correct.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                      +-------------------------------------------+\r\n" );
document.write( "                      |   The correct setup would be AS FOLLOWS   |\r\n" );
document.write( "                      +-------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Let x be the Sharon present age.\r\n" );
document.write( "\r\n" );
document.write( "Then 5 years ago Sharon's age was (x-5) years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The Kate's age in 5 years will be  90 - (x+5);\r\n" );
document.write( "\r\n" );
document.write( "hence, the Kate's age 5 years back was  (90 - (x+5) - 10) = 80-(x+5) years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we can write equation describing the ratio of their ages 5 years back\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    \"%2880-%28x%2B5%29%29%2F%28x-5%29\" = \"4%2F3\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now we can solve it, first cross-multiplying\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    3*(80-(x+5)) = 4*(x-5)\r\n" );
document.write( "\r\n" );
document.write( "    240 - 3x - 15 = 4x - 20\r\n" );
document.write( "\r\n" );
document.write( "    240 - 15 + 20 = 4x + 3x\r\n" );
document.write( "\r\n" );
document.write( "         245      = 7x\r\n" );
document.write( "\r\n" );
document.write( "          x       = 245/7 = 35.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The Sharon's present age is 35 years.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.   In 5 years, Sharon will be 35+5 = 40 years old;  Kate will be 90-40 = 50 years old; hence, Kate is 45 years old now.\r\n" );
document.write( "\r\n" );
document.write( "         5 years ago, Sharon was 35-5 = 30 years old, while Kate was 45-5 = 40 years old, and the ratio of their ages 5 years ago was really  \"40%2F30\" = \"4%2F3\".\r\n" );
document.write( "\r\n" );
document.write( "         The check  confirms that my solution is correct.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );