document.write( "Question 1062665: A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank. \n" ); document.write( "
Algebra.Com's Answer #677682 by ikleyn(52788)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10,
\n" ); document.write( "find the number of dimes in the bank.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This problem is for ONE unknown. Not for 3 !!\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Let \"n\" be the number of nickels.\r\n" );
document.write( "\r\n" );
document.write( "Then the number of pennies is (n+8) and the number of dimes is (n+3).\r\n" );
document.write( "\r\n" );
document.write( "Each penny contributes 1 cent to the total. In all, (n+8) pennies contribute (n+8) cents to the total.\r\n" );
document.write( "\r\n" );
document.write( "Each nickel contributes 5 cents to the total. \"n\" nickels contribute 5n cents to the total.\r\n" );
document.write( "\r\n" );
document.write( "Each dime contributes 10 cents to the total. (n+3) dimes contribute 10(n+3) cents to the total.\r\n" );
document.write( "\r\n" );
document.write( "Therefore, your \"value\" equation is \r\n" );
document.write( "\r\n" );
document.write( "(n+8) + 5n + 10(n+3) = 310 cents.\r\n" );
document.write( "\r\n" );
document.write( "n + 8 + 5n + 10n + 30 = 310,\r\n" );
document.write( "\r\n" );
document.write( "16n + 38 = 310  --->  16n = 310-38  --->  16n = 272  --->  n = \"272%2F16\" = 17.\r\n" );
document.write( "\r\n" );
document.write( "Thus the number of nickels is 17.\r\n" );
document.write( "\r\n" );
document.write( "Then the number of pennies is (17+8) = 25  and  the number of dimes is (17+3) = 20.\r\n" );
document.write( "\r\n" );
document.write( "Check. 25 + 17*5 + 10*20 = \r\n" );
document.write( "\r\n" );
document.write( "Answer.  The number of pennies is 25, the number of nickels is 17  and  the number of dimes is 20.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The lesson to learn from the solution: This problem is for ONE unknown. Not for 3 !!\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "When you solve the problems like this one, your first step is to select a major unknown.
\n" ); document.write( "Then you express other unknowns via the major one.
\n" ); document.write( "Then you construct your equation.
\n" ); document.write( "Then you solve it.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For coin problems and their detailed solutions see the lessons in this site:\r
\n" ); document.write( "\n" ); document.write( "    - Coin problems\r
\n" ); document.write( "\n" ); document.write( "    - More Coin problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving coin problems without using equations\r
\n" ); document.write( "\n" ); document.write( "    - Kevin and Randy Muise have a jar containing coins\r
\n" ); document.write( "\n" ); document.write( "    - Typical coin problems from the archive\r
\n" ); document.write( "\n" ); document.write( "    - Solving coin problems mentally by grouping without using equations\r
\n" ); document.write( "\n" ); document.write( "    - Santa Claus helps solving coin problem\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them attentively and become an expert in this field.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Coin problems\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "To make you laugh, I'll show you another approach which allows to solve the problem without using equations.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For the moment, take out 8 pennies and 3 dimes from the collection (mentally, of course).\r\n" );
document.write( "\r\n" );
document.write( "Then you have equal number of pennies, nickels and dimes, and the collection is worth 310 - 8 - 30 = 272 cents.\r\n" );
document.write( "\r\n" );
document.write( "Hence, you can group the remaining coins in sets (1 penny, 1 nickel, 1 dime) each.\r\n" );
document.write( "\r\n" );
document.write( "Each such set is worth 1 + 5 + 10 = 16 cents.\r\n" );
document.write( "\r\n" );
document.write( "How many such sets do you have ? - But of course, \"272%2F16\" = 17.\r\n" );
document.write( "\r\n" );
document.write( "Hence you have 17 nickels in your collection.\r\n" );
document.write( "\r\n" );
document.write( "And so on . . . \r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved (two times).\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );