document.write( "Question 1200476: A piggy bank contains only nickels, dimes, and quarters. If there are 76 coins worth $8.50, and there are twice as many dimes as nickels, how many of each coin are there?
\n" ); document.write( "Show all of your work.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #834620 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A piggy bank contains only nickels, dimes, and quarters.
\n" ); document.write( "If there are 76 coins worth $8.50, and there are twice as many dimes as nickels,
\n" ); document.write( "how many of each coin are there?
\n" ); document.write( "Show all of your work.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        It is a typical problem to be solved by reduction
\n" ); document.write( "        to one single equation in one single unknown.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        See how simple the solution is.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let x be the number of nickels.\r\n" );
document.write( "\r\n" );
document.write( "Then the number of dimes is 2x, \r\n" );
document.write( "\r\n" );
document.write( "and the number of quarters is  (76 - x - 2x) = (76-3x).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now write the total money equation\r\n" );
document.write( "\r\n" );
document.write( "    5x + 10*(2x) + 25*(76-3x) = 850  cents.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and find x\r\n" );
document.write( "\r\n" );
document.write( "    5x + 20x + 25*76 - 25*(3x) = 850\r\n" );
document.write( "\r\n" );
document.write( "    5x + 20x + 1900  -  75x    = 850\r\n" );
document.write( "\r\n" );
document.write( "         -50x                  = 850 - 1900\r\n" );
document.write( "\r\n" );
document.write( "         -50x                  =   -1050\r\n" );
document.write( "\r\n" );
document.write( "            x                  =   =  =  = 21.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  21 nickels,  2*21 = 42 dimes, and the rest of coins, 76-21-42 = 13, are quarters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.   Total cents is  21*5 + 42*10 + 13*25 = 850,  correct.\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( "From the first glance, this problem is for 3 unknowns.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "But, actually, it can be solved using only one unknown and one single equation.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "There is no need to explain that obvious fact that it reduces the volume of calculations, \r
\n" ); document.write( "\n" ); document.write( "reduces your efforts and diminish the chances to make errors.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In addition, it is a good style to solve the problem in this way.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Therefore, from my post learn how to do it.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You also should learn to recognize such problems from the first glance.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "At this site, there is a SPECIAL LESSON explaining and showing different similar problems solved in the same way\r
\n" ); document.write( "\n" ); document.write( " - Advanced word problems to solve using a single linear equation\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Remember, that your task is not simply to get a correct answer, only.\r
\n" ); document.write( "\n" ); document.write( "Your task is to do it in a right way ( ! )\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Happy learning ( ! )\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );