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.  
<pre>Let number of nickels, dimes, and quarters be x, y, and z, respectively
Then we get the following: "number of coins" equation: x + y + z = 131 
"Coin-comparison" equation: z = y + 10_____y - z = - 10
"Money-value" equation: .05x + .1y + .25z = 21.55
x + 2y + 5z = 431 -------- Multiplying by 20 to make all coefficients and constant, integers
This gives us: 
x +  y +  z =  131 ------- eq (i)
     y -  z = - 10 ------- eq (ii)
x + 2y + 5z =  431 ------- eq (iii)
We take the coefficients on the variables in each equation, along with their constants to get the following AUGMENTED matrix:
{{{(highlight(highlight_green(matrix(3,5, 1, 1, 1, "|", 131,
0, 1, - 1, "|", - 10,
1, 2, 5, "|", 431))))}}}