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.
Found 2 solutions by jorel555, MathTherapy:
Answer by jorel555(1290)   (Show Source):
You can put this solution on YOUR website! Let n be nickels, d be dimes, and q be quarters. Then:
n+d+q=131
q=d+10
5n+10d+25q=2155. So we have two equations
n+d+d+10=n+2d=131
5n+10d+25(d+10)=5n+35d=1905. ☺☺☺☺
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website!
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.
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:
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