document.write( "Question 1202774: In what ways can you change a $100 bill using $10 bills, $5 bills, and $1 bills? \n" ); document.write( "
Algebra.Com's Answer #837866 by greenestamps(13200)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "Whether you really want a list of all the different ways, or whether you only want to know HOW MANY ways there are, I will show you HOW to solve the problem and leave the details to you.

\n" ); document.write( "(1) Since the $10 bills and $5 bills together make a total number of dollars that is a multiple of 5, and since the total $100 is a multiple of 5, the total value of the $1 bills must be a multiple of 5.

\n" ); document.write( "(2) For each number of $1 bills that is a multiple of 5, the number of ways to make change for $100 is determined by the number of $10 bills you can have. For example, if there are 55 $1 bills, then the remaining amount is $45, and you can use 0, 1, 2, 3, or 4 $10 bills, making up the rest with $5 bills. That makes 5 ways to make change for $100 if the number of $1 bills is 55.

\n" ); document.write( "To outline the complete solution, then....
\r\n" );
document.write( "column 1: # of $1 bills\r\n" );
document.write( "column 2: remaining amount\r\n" );
document.write( "column 3: # of choices for the number of $10 bills\r\n" );
document.write( "\r\n" );
document.write( "   0   100   11   (0 to a maximum of 10)\r\n" );
document.write( "   5    95   10   (0 to a maximum of 9)\r\n" );
document.write( "  10    90   10   (0 to a maximum of 9)\r\n" );
document.write( "  ...\r\n" );
document.write( "  ...\r\n" );
document.write( "  85    15    2   (0 to a maximum of 1)\r\n" );
document.write( "  90    10    2   (0 to a maximum of 1)\r\n" );
document.write( "  95     5    1   (only 0)\r\n" );
document.write( " 100     0    1   (only 0)

\n" ); document.write( "Add the numbers in column 3 to find the total number of ways of making change for $100 using $10, $5, and $1 bills.

\n" ); document.write( "Note there is a nice pattern in the numbers in column 3 that makes it possible to find the total without adding the numbers one at a time....

\n" ); document.write( " \n" ); document.write( "
\n" );