document.write( "Question 1053484: You have 131 coins in nickels dimes and quarters with a combined value of $21.55. There are 10 more quarters than dimes. Write an augmented matrix to represent the situation. \n" ); document.write( "

Algebra.Com's Answer #668795 by MathTherapy(10559) $\"\"$ $\"About$

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\n" ); document.write( "You have 131 coins in nickels dimes and quarters with a combined value of $21.55. There are 10 more quarters than dimes. Write an augmented matrix to represent the situation.
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Let number of nickels, dimes, and quarters be x, y, and z, respectively
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document.write( "Then we get the following: \"number of coins\" equation: x + y + z = 131 
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document.write( "\"Coin-comparison\" equation: z = y + 10_____y - z = - 10
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document.write( "\"Money-value\" equation: .05x + .1y + .25z = 21.55
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document.write( "x + 2y + 5z = 431 -------- Multiplying by 20 to make all coefficients and constant, integers
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document.write( "This gives us: 
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document.write( "x +  y +  z =  131 ------- eq (i)
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document.write( "     y -  z = - 10 ------- eq (ii)
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document.write( "x + 2y + 5z =  431 ------- eq (iii)
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document.write( "We take the coefficients on the variables in each equation, along with their constants to get the following AUGMENTED matrix:
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