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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document.write( "Use a matrix \n" );
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Algebra.Com's Answer #665007 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! n = no. of nickels \n" ); document.write( "d = no. of dimes \n" ); document.write( "q = no. of quarters \n" ); document.write( ": \n" ); document.write( "Write an equation for each statement, \n" ); document.write( ": \n" ); document.write( "A coin bank contains 27 coins, all nickels, dimes, or quarters. \n" ); document.write( "n + d + q = 27 \n" ); document.write( ": \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 \n" ); document.write( ": \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 \n" ); document.write( ": \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 \n" ); document.write( ": \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 \n" ); document.write( ": \n" ); document.write( ": \n" ); document.write( "Check this in the 3rd equaton \n" ); document.write( ".10(5) + .25(14) = 4 \n" ); document.write( ".50 + 3.50 = 4 \n" ); document.write( ": \n" ); document.write( ": \n" ); document.write( "A long journey but we finally got it. Hope this made sense to you. CK \n" ); document.write( " |