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Question 271947: I am studying matrices, but have a hard time translating word problems. How would you set this up in a matrix?
On counting the money in her piggy bank, Sally found that she had 122 coins, all nickels, dimes, and quarters. If the total value of the coins was $15, and the total value of the quarters was 4 times the total value of the nickels, how many of each kind of coin did Sally have?
Thanks in advance!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! First write an equation for each statement
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On counting the money in her piggy bank, Sally found that she had 122 coins, all nickels, dimes, and quarters.
n + d + q = 122
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If the total value of the coins was $15,
.05n + .10d + .25q = 15.00
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and the total value of the quarters was 4 times the total value of the nickels,
.25q = 4(.05n)
.25q = .20n
-.20n + .25q = 0
We want it in this form for the matrix
-.20n + 0d + .25q = 0
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Here is the matrix from these three equations
1 + 1 + 1 = 122
.05 + .1 + .25 = 15
-.2 + 0 + .25 = 0
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Using the matrix feature in my Ti83, I got
n = 40
d = 50
q = 32
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