document.write( "Question 552424: Shady Grady finds a parking meter with a broken lock and scoops out the change inside. Then meter accepts nickels, dimes, and quarters, and there were 32 coins inside with a total value of $6.80. How many of each type of coin did Grady get?
\n" ); document.write( "I can only get two equations and i think i need 3 to solve? \n" ); document.write( "
Algebra.Com's Answer #360285 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
you are correct.
\n" ); document.write( "you need 3 equations in 3 unknowns to get an exact answer.
\n" ); document.write( "with 2 equations in 3 unknowns, you would have to solve for 2 of the variables in terms of one of the variables and then make assumptions about the that variable that would fix the value of the other 2 variables.
\n" ); document.write( "i did that with this problem and got the following:
\n" ); document.write( "n = 6 - .75d
\n" ); document.write( "q = 26 - .25d
\n" ); document.write( "from that, i made assumptions about the number of dime and got the following:
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document.write( "dimes	nickels	quarters	coins	money	invalid\r\n" );
document.write( "					\r\n" );
document.write( "0	6	26	32	$6.80	\r\n" );
document.write( "4	3	25	32	$6.80	\r\n" );
document.write( "8	0	24	32	$6.80	\r\n" );
document.write( "12	-3	23	32	$6.80	*****\r\n" );
document.write( "16	-6	22	32	$6.80	*****\r\n" );
document.write( "20	-9	21	32	$6.80	*****\r\n" );
document.write( "24	-12	20	32	$6.80	*****\r\n" );
document.write( "28	-15	19	32	$6.80	*****\r\n" );
document.write( "32	-18	18	32	$6.80	*****\r\n" );
document.write( "36	-21	17	32	$6.80	*****\r\n" );
document.write( "40	-24	16	32	$6.80	*****\r\n" );
document.write( "44	-27	15	32	$6.80	*****\r\n" );
document.write( "48	-30	14	32	$6.80	*****\r\n" );
document.write( "52	-33	13	32	$6.80	*****\r\n" );
document.write( "56	-36	12	32	$6.80	*****\r\n" );
document.write( "60	-39	11	32	$6.80	*****\r\n" );
document.write( "64	-42	10	32	$6.80	*****\r\n" );
document.write( "68	-45	9	32	$6.80	*****\r\n" );
document.write( "

\n" ); document.write( "when creating the table, it became apparent that i needed to increment the number of dimes in groups of 4 to get integer values for the other coins.
\n" ); document.write( "all possible combinations gave me 32 coins for a total of $6.80, but the ones marked as invalid did this by using negative values of coins.
\n" ); document.write( "for example:
\n" ); document.write( "with 68 dimes, i got -45 nickels and 9 quarters.
\n" ); document.write( "68 - 45 + 9 = 32
\n" ); document.write( "68*10 - 45*.05 + 9*.25 = 6.80 - 2.25 + 2.25 = 6.80
\n" ); document.write( "the numbers came out right but only if the number of nickels was negative which can't be so the answer was marked as invalid.
\n" ); document.write( "the possible answers became the first 3 in the list.
\n" ); document.write( "there would be no way to narrow it down further than that without some additional information being provided such as the number of dimes being 0, 4, or 8.\r
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