document.write( "Question 1049416: I don't understand how to set up this systems of equations. A coin bank contains 27 coins, all nickels, dimes, or quarters. The combined value of the nickels and dimes is $0.90. The combined value of the dimes and quarters is $4. How many coins of each type are in the bank?
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Algebra.Com's Answer #665007 by ankor@dixie-net.com(22740)\"\" \"About 
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n = no. of nickels
\n" ); document.write( "d = no. of dimes
\n" ); document.write( "q = no. of quarters
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\n" ); document.write( "Write an equation for each statement,
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\n" ); document.write( "A coin bank contains 27 coins, all nickels, dimes, or quarters.
\n" ); document.write( "n + d + q = 27
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\n" ); document.write( " The combined value of the nickels and dimes is $0.90.
\n" ); document.write( ".05n + .10d = .90
\n" ); document.write( ":
\n" ); document.write( " The combined value of the dimes and quarters is $4.00
\n" ); document.write( ".10d + .25q = 4.0
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\n" ); document.write( "How many coins of each type are in the bank?
\n" ); document.write( " Use elimination on the last two equations
\n" ); document.write( " 0n + .10d + .25q = 4.00
\n" ); document.write( ".05n + .10d + 0q = 0.90
\n" ); document.write( "--------------------------Subtraction eliminates d
\n" ); document.write( "-.05n +.25q = 3.10
\n" ); document.write( ".25q = .05n + 3.10
\n" ); document.write( "multiply equation by 4
\n" ); document.write( "1q = .20n + 12.40
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\n" ); document.write( "Substitute for q in the first equation
\n" ); document.write( "n + d + .2n + 12.40 = 27
\n" ); document.write( "1.2n + d = 14.60
\n" ); document.write( "d = -1.2n + 14.60
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\n" ); document.write( "Substitute for d in the 2nd equation
\n" ); document.write( ".05n + .10(-1.2n+14.60) = .90
\n" ); document.write( ".05n - .12n - 1.46 = .90
\n" ); document.write( "-.07n = .90 - 1.46
\n" ); document.write( "-.07n = -.56
\n" ); document.write( "n = -.56/-.07
\n" ); document.write( "n = + 8 nickels
\n" ); document.write( "then
\n" ); document.write( "q = .20(8) + 12.40
\n" ); document.write( "q = 1.6 + 12.4
\n" ); document.write( "q = 14 quarters
\n" ); document.write( "and using the 1st equation
\n" ); document.write( "8 + d + 14 = 27
\n" ); document.write( "d = 27 - 22
\n" ); document.write( "d = 5 dimes
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\n" ); document.write( "Check this in the 3rd equaton
\n" ); document.write( ".10(5) + .25(14) = 4
\n" ); document.write( ".50 + 3.50 = 4
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\n" ); document.write( "A long journey but we finally got it. Hope this made sense to you. CK
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