document.write( "Question 251225: I have $2.35 in nickles and dimes . If i have a total of 23 coins , how many of each coin do i have ? \n" ); document.write( "
Algebra.Com's Answer #182940 by oberobic(2304)\"\" \"About 
You can put this solution on YOUR website!
In solving coin problems, you have to keep track of the number of coins and the value of the coins.
\n" ); document.write( "n = number of nickels
\n" ); document.write( "5n = value of the nickels in cents
\n" ); document.write( "d = number of dimes
\n" ); document.write( "10d = value of the dimes in cents
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\n" ); document.write( "We are told n+d = 23 coins.
\n" ); document.write( "We are told that 5n + 10d = 235 cents.
\n" ); document.write( ".
\n" ); document.write( "We can solve these two equations in several ways. An obvious approach is to set n = 23-d and then substitute.
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\n" ); document.write( "5(23-d) + 10d = 235
\n" ); document.write( "115 - 5d + 10d = 235
\n" ); document.write( "5d = 120
\n" ); document.write( "d = 24
\n" ); document.write( ".
\n" ); document.write( "n + d = 23
\n" ); document.write( "n = -1
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\n" ); document.write( "Checking our values:
\n" ); document.write( "5n = 5*-1 = -5 cents
\n" ); document.write( "24d = 10*24 = 240 cents
\n" ); document.write( "Adding: 235 cents.
\n" ); document.write( ".
\n" ); document.write( "But this is a nonsensical answer. You cannot have -1 nickels.
\n" ); document.write( ".
\n" ); document.write( "Using a 'brute force' approach, it is easy to see that the maximum value of 23 coins occurs with 22 dimes and 1 nickel...and it is 225 cents ($2.25), which is less than the stated amount.
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document.write( "n	d	n+d	5n	10d	5n+10d\r\n" );
document.write( "1	22	23	5	220	225\r\n" );
document.write( "2	21	23	10	210	220\r\n" );
document.write( "3	20	23	15	200	215\r\n" );
document.write( "4	19	23	20	190	210\r\n" );
document.write( "5	18	23	25	180	205\r\n" );
document.write( "6	17	23	30	170	200\r\n" );
document.write( "7	16	23	35	160	195\r\n" );
document.write( "8	15	23	40	150	190\r\n" );
document.write( "9	14	23	45	140	185\r\n" );
document.write( "10	13	23	50	130	180\r\n" );
document.write( "11	12	23	55	120	175\r\n" );
document.write( "12	11	23	60	110	170\r\n" );
document.write( "13	10	23	65	100	165\r\n" );
document.write( "14	9	23	70	90	160\r\n" );
document.write( "15	8	23	75	80	155\r\n" );
document.write( "16	7	23	80	70	150\r\n" );
document.write( "17	6	23	85	60	145\r\n" );
document.write( "18	5	23	90	50	140\r\n" );
document.write( "19	4	23	95	40	135\r\n" );
document.write( "20	3	23	100	30	130\r\n" );
document.write( "21	2	23	105	20	125\r\n" );
document.write( "22	1	23	110	10	120\r\n" );
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\n" ); document.write( ".
\n" ); document.write( "So there is no solution to the problem. \n" ); document.write( "
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