document.write( "Question 71997: I have a purse with several coins in it. The coins have values of 1 cent, 5 cents, 10 cents, and 25 cents. The average value of all coins in the purse is 17 cents. If I take out one 1 cent coin, the average value of all coins in the purse becomes 18 cents. How many of each coin are there in the purse? Can you please help? \n" ); document.write( "
Algebra.Com's Answer #51490 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
I have a purse with several coins in it. The coins have values of 1 cent,
\n" ); document.write( "5 cents, 10 cents, and 25 cents. The average value of all coins in the purse
\n" ); document.write( " is 17 cents. If I take out one 1 cent coin, the average value of all coins in
\n" ); document.write( " the purse becomes 18 cents. How many of each coins are there in the purse?
\n" ); document.write( " Can you please help?
\n" ); document.write( ":
\n" ); document.write( "\"%281w+%2B+5x+%2B+10y+%2B+25z%29%2F%28w+%2B+x+%2B+y+%2B+z%29\" = 17
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\n" ); document.write( "\"%281%28w-1%29+%2B+5x+%2B+10y+%2B+25z%29%2F%28%28w-1%29+%2B+x+%2B+y+%2B+z%29\" = 18
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\n" ); document.write( "Note the difference in the two equations is 1:
\n" ); document.write( "Let t = total value of the coins originally:
\n" ); document.write( "Let c = number of coins number of coins originally:
\n" ); document.write( "\"t%2Fc%29\" = 17
\n" ); document.write( " t = 17c
\n" ); document.write( "and the removal of 1 cent:
\n" ); document.write( "\"%28t-1%29%2F%28c-1%29\" = 18
\n" ); document.write( "t - 1 = 18(c-1)
\n" ); document.write( "t - 1 = 18c - 18
\n" ); document.write( "t = 18c - 18 + 1
\n" ); document.write( "t = 18c - 17
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\n" ); document.write( "Substitute 17c for t and solve for c
\n" ); document.write( "17c = 18c - 17
\n" ); document.write( "17c - 18c = -17
\n" ); document.write( "-c = -17
\n" ); document.write( "c = 17 coins originally
\n" ); document.write( ":
\n" ); document.write( "Find t: t = 17c
\n" ); document.write( "t = 17*17
\n" ); document.write( "t = 289 cents, total value originally
\n" ); document.write( ":
\n" ); document.write( "After removing 1 penny:
\n" ); document.write( "288/16 = 18 cents, as the problem states
\n" ); document.write( ":
\n" ); document.write( "At least we know the total and the number of coins now:
\n" ); document.write( "1W + 5x + 10y + 25z = 289
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\n" ); document.write( "From this we can see that there has to be at least 4 pennies, we have:
\n" ); document.write( "5x + 10y + 25z = 285; subtracted the 4 cents
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\n" ); document.write( "We know there has to be at least 1 nickel then:
\n" ); document.write( "10y + 25z = 280; subtracted the nickel
\n" ); document.write( ":
\n" ); document.write( "We know there has to be at least 3 dimes then:
\n" ); document.write( "25z = 250; subtracted the value of 3 dimes
\n" ); document.write( "z = 250/25
\n" ); document.write( "z = 10 quarters + 3 dimes + 1 nickel + 4 pennies, that's 18 coins!!
\n" ); document.write( "But we found that there should only be 17 coins originally!
\n" ); document.write( ":
\n" ); document.write( "We can have 11 quarters, 2 nickels and 4 pennies, that 17 coins, however we
\n" ); document.write( "don't have any dimes so I am not sure if this is a solution or not
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\n" ); document.write( "Check it anyway:
\n" ); document.write( "11 * 25 = 275
\n" ); document.write( " 2 * 5 = 10
\n" ); document.write( " 4 * 1 = 4
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\n" ); document.write( "17 coins=289 cents
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\n" ); document.write( "I'm not sure if there is a solution using dimes, perhaps this will help you anyway.
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\n" ); document.write( "I would appreciate it, if you would let me know what you find out about this problem. ankor@dixie-net.com\r
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