document.write( "Question 990357: Why is it that when you have a number (context of money) for example £64.83 and swap the pounds and pence, eg. £83.64 then add those together....£148.47 then swap the tens and ones with tenths and hundredths again, eg. £147.48 and add THOSE numbers.....£295.95 the tens and ones number is the same as the tenths and hundredths number? \n" ); document.write( "
Algebra.Com's Answer #610623 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
It is not always so. It works half of the time. It all depends on the digits.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you start with 67.89, it does not work.
\n" ); document.write( "The first swap gives you 89.67;
\n" ); document.write( "the first sum is 157.56, which reversed is 156.57,
\n" ); document.write( "and the second sum is 314.13.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you start with 34.25, it does not work either.
\n" ); document.write( "The first swap gives you 25.34;
\n" ); document.write( "the first sum is 59.59, which reversed is also 59.59,
\n" ); document.write( "and the second sum is 119.18.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It worked for your example.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you start with 14.26, it also works.
\n" ); document.write( "The first swap gives you 26.14;
\n" ); document.write( "the first sum is 40.40, which reversed is also 40.40,
\n" ); document.write( "and the second sum is 80.80.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"p\"= number of whole pounds, with \"p%3C=99\"
\n" ); document.write( "\"c\"= number of cents, with \"c%3C=99\"
\n" ); document.write( "The amount value, in cents, is \"100p%2Bc\" .
\n" ); document.write( "Swapping the numbers of pounds and cents, we have a value of \"100c%2Bp\" .
\n" ); document.write( "Adding both values, we get \"100p%2Bc%2B100c%2Bp=100%28p%2Bc%29%2B%28p%2Bc%29\" .
\n" ); document.write( "From then on, it all depends on the value of \"p%2Bc\" .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If \"p%2Bc%3C=49%3C99\", it works.
\n" ); document.write( "For the first sum,
\n" ); document.write( "\"p%2Bc\" is the two-digit number that makes up the tens and ones, and
\n" ); document.write( "\"p%2Bc\" is also the two-digit number that makes up the cents (the tenths and hundredths).
\n" ); document.write( "Then, swapping the tens and ones with tenths and hundredths gives you the same number.
\n" ); document.write( "Adding swapped and unswapped, you get
\n" ); document.write( "\"100%28p%2Bc%29%2B%28p%2Bc%29%2B100%28p%2Bc%29%2B%28p%2Bc%29=100%282p%2B2c%29%2B%282p%2B2c%29\" .
\n" ); document.write( "Since \"p%2Bc%3C=49\" , \"2p%2B2c%3C=98\" ,
\n" ); document.write( "\"2p%2B2c\" is a two-digit number that makes up the tens and ones, and
\n" ); document.write( "\"2p%2B2c\" is also the two-digit number that makes up the cents (the tenths and hundredths).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If \"50%3C=p%2Bc%3C=99\", as in the case of 34.25, it does not work.
\n" ); document.write( "For the first sum,
\n" ); document.write( "\"p%2Bc\" is a two-digit number that makes up the tens and ones, and
\n" ); document.write( "\"p%2Bc\" is also the two-digit number that makes up the cents (the tenths and hundredths).
\n" ); document.write( "Then, swapping the tens and ones with tenths and hundredths gives you the same number.
\n" ); document.write( "Adding swapped and unswapped, you get
\n" ); document.write( "\"100%28p%2Bc%29%2B%28p%2Bc%29%2B100%28p%2Bc%29%2B%28p%2Bc%29=100%282p%2B2c%29%2B%282p%2B2c%29\" .
\n" ); document.write( "Since \"50%3C=p%2Bc%3C=99\" , \"100%3C=2p%2B2c%3C=198\" ,
\n" ); document.write( "\"2p%2B2c=100%2B%282p%2B2c-100%29\" is a three-digit number,
\n" ); document.write( "but \"%282p%2B2c-100%29%3C=98\" and is a two-digit number.
\n" ); document.write( "The second sum is
\n" ); document.write( " .
\n" ); document.write( "\"%282p%2B2c-100%29\" is a two-digit number that represents the cents,
\n" ); document.write( " cents represents the \"1\" in the hundreds place.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If \"100%3C=p%2Bc%3C=149\", as in the case of 83.64, it works.
\n" ); document.write( "The first sum is
\n" ); document.write( " , where
\n" ); document.write( "\"p%2Bc-100\" is the two-digit number that makes up the cents (the tenths and hundredths),
\n" ); document.write( "\"p%2Bc-100%2B1\" is the two-digit number that makes up the tens and ones,
\n" ); document.write( "and the \"10000\" cents represents the \"1\" in the hundreds place.
\n" ); document.write( "Swapping the tens and ones with tenths and hundredths yields
\n" ); document.write( "\"10000%2B100%28p%2Bc-100%29%2B%28p%2Bc-100%2B1%29\" cents.
\n" ); document.write( "Adding swapped and unswapped we get (in cents)
\n" ); document.write( " .
\n" ); document.write( "Since \"100%3C=p%2Bc%3C=149\" , \"200%3C=2p%2B2c%3C=298\" ,
\n" ); document.write( "and \"1%3C=2p%2B2c-200%2B1%3C=99\" is the two digit number that
\n" ); document.write( "makes up the tens and ones, and also makes up the tenths and hundredths.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If \"150%3C=p%2Bc%3C=198\" , as in the case of 67.89, it does not work.
\n" ); document.write( "The first sum is
\n" ); document.write( "\"10000%2B100%28p%2Bc-100%2B1%29%2B%28p%2Bc-100%29\" , where
\n" ); document.write( "\"p%2Bc-100\" is the two-digit number that makes up the cents (the tenths and hundredths),
\n" ); document.write( "\"p%2Bc-100%2B1\" is the two-digit number that makes up the tens and ones,
\n" ); document.write( "and the \"10000\" cents represents the \"1\" in the hundreds place.
\n" ); document.write( "Swapping the tens and ones with tenths and hundredths yields
\n" ); document.write( "\"10000%2B100%28p%2Bc-100%29%2B%28p%2Bc-100%2B1%29\" cents.
\n" ); document.write( "Adding swapped and unswapped we get (in cents)
\n" ); document.write( "\"20000%2B100%282p%2B2c-200%2B1%29%2B%282p%2B2c-200%2B1%29\" .
\n" ); document.write( "However, since \"150%3C=p%2Bc%3C=198\",
\n" ); document.write( "\"300%3C=2p%2B2c%3C=396\" , and \"101%3C=2p%2B2c-200%2B1%3C=197\" ,
\n" ); document.write( "so the second sum is
\n" ); document.write( "
\n" ); document.write( "=\"30000%2B100%282p%2B2c-300%2B2%29%2B%282p%2B2c-300%2B1%29\" , where
\n" ); document.write( "\"%282p%2B2c-300%2B1%29\" is the two-digit number that makes up the cents (the tenths and hundredths),
\n" ); document.write( "\"%282p%2B2c-300%2B1%29\" is the two-digit number that makes up the tens and ones,
\n" ); document.write( "and the \"30000\" cents represents the \"3\" in the hundreds place. \n" ); document.write( "
\n" );