document.write( "Question 1101101: Bruce collects stamps. He has six times as many 10-cent stamps as 5-cent stamps, and he has some 20 cent stamps as well. Bruce has 72 stamps with a total value of $8.40. How many of each stamp does he have? \n" ); document.write( "

Algebra.Com's Answer #715673 by ikleyn(52835) $\"\"$ $\"About$

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

\r\n" );
document.write( "Bruce has\r\n" );
document.write( "\r\n" );
document.write( "(x of 5-cent stumps) + (6x 10-cent stamps) + (y 20-cent stumps)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, you have these two equations:\r\n" );
document.write( "\r\n" );
document.write( "(1)  x  + 6x      +    y =  72           (counting stamps)\r\n" );
document.write( "(2)  5x + 10*(6x) + 20*y = 840  cents    (counting stamps' values) \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify the equations\r\n" );
document.write( "\r\n" );
document.write( "(1)   7x +   y =  72,\r\n" );
document.write( "(2)  65x + 20y = 840.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From (1), express  y = 72-7x  and substitute it into eq(2). You will get\r\n" );
document.write( "\r\n" );
document.write( "65x + 20*(72-7x) = 840  ====>\r\n" );
document.write( "\r\n" );
document.write( "65x + 1440 - 140x = 840  ====>\r\n" );
document.write( "\r\n" );
document.write( "-75x = 840 - 1440 = -600  ====>  x =  = 8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, Bruce has  8  5-cent stamps;  8*6 = 48  10-cent stamps  and  72 - (8+48) = 16    20-cent stamps.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.  Bruce has  8  5-cent stamps;  48  10-cent stamps  and  16  20-cent stamps.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Check.  5*8 + 10*48 + 20*16 = 840.  ! Correct !\r\n" );
document.write( "

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

\n" );