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Question 345680: Need help with systems of equations using matrices.
Don't know how to set up this problem.
A change machine contains nickels, dimes, and quarters. There are 75 coins in the machine and the value of the coins is $7.25. If there are 5 times as many nickels as dimes, find the number of coins of each type in the machine.
Need by 9pm tonight (if possible). Thank you for your time.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A change machine contains nickels, dimes, and quarters.
There are 75 coins in the machine and the value of the coins is $7.25.
If there are 5 times as many nickels as dimes,
find the number of coins of each type in the machine.
;
Write an equation for each statement:
:
"There are 75 coins in the machine"
n + d + q = 75
:
"the value of the coins is $7.25."
.05 + .10d + .25q = 7.25
:
"there are 5 times as many nickels as dimes"
n = 5d
Arrange in the same form
n - 5d = 0
:
Using the coefficients of these 3 equations, write a matrix
(in the 3rd equation q=0
:
1, 1, 1, 75
.05, .10, .25, 7.25
1 - 5, 0, 0
:
Solve this 3 by 4 matrix using your favorite method
:
My favorite is the matrix feature on the Ti83, I got
n = 50
d = 10
q = 15
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