document.write( "Question 974752: a box contains $7.15 in nickels, dimes, and quaters,. There are 42 coins in all and the combined total of nickles and dimes is 2 less than the total number of quaters. Find the number of each type of coin, using systems of equations, and showing work. \n" ); document.write( "

Algebra.Com's Answer #596596 by MathTherapy(10552) $\"\"$ $\"About$

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\n" ); document.write( "a box contains $7.15 in nickels, dimes, and quaters,. There are 42 coins in all and the combined total of nickles and dimes is 2 less than the total number of quaters. Find the number of each type of coin, using systems of equations, and showing work.
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Let number of nickels, dimes, and quarters, be N, D, and Q, respectively
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document.write( "Then we get: N + D + Q = 42 ------- eq (i)
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document.write( "Also, N + D = Q - 2_____N + D - Q = - 2 ------- eq (ii)
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document.write( "2Q = 44 ------ Subtracting eq (ii) from eq (i) 
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document.write( "Q, or number of quarters = , or \r
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document.write( "N + D + 22 = 42 ------- Substituting 22 for Q in eq (i)
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document.write( "N + D = 20
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document.write( "N = 20 - D\r
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document.write( "Since all coins total $7.15, we then get:
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document.write( ".05N + .1D + .25(Q) = 7.15
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document.write( ".05(20 - D) + .1D + .25(22) = 7.15	
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document.write( "1 - .05D + .1D + 5.5 = 7.15	
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document.write( "- .05D + .1D + 1 + 5.5 = 7.15	
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document.write( ".05D + 6.5 = 7.15
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document.write( ".05D = .65
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document.write( "D, or number of dimes = , or 
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document.write( "N = 20 - D 
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document.write( "N = 20 - 13 ------ Substituting 13 for D
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document.write( "N, or number of nickels =  \n" );
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