SOLUTION: The number of nickels in a coin box is 8 more than the number of quarters and the number of dimes is 3 times the number of nickels. Find the number of each kind of coin if their to

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Question 829677: The number of nickels in a coin box is 8 more than the number of quarters and the number of dimes is 3 times the number of nickels. Find the number of each kind of coin if their total value is $7.00
Found 2 solutions by TimothyLamb, LinnW:
Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website!
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5x + 10y + 25z = 700
x = z + 8
y = 3x
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put the system of linear equations into standard form:
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5x + 10y + 25z = 700
x - z = 8
3x - y = 0
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copy and paste the above linear system in standard form into this matrix-method solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = nickels = 15
y = dimes = 45
z = quarters = 7
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system matrix
5 10 25
1 0 -1
3 -1 0
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inverse of system matrix
0.016666667 0.41666667 0.16666667
0.05 1.25 -0.5
0.016666667 -0.58333333 0.16666667
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determinant of system matrix = -60
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Answer by LinnW(1048) (Show Source):
You can put this solution on YOUR website!
Set n = no of nickles
d = no of dimes
q = no of quarters
n = q + 8
for the equation above solve for q.
subtract 8 from each side
n - 8 = q or
q = n - 8
d = 3n
We know that
(no of dimes)(0.10) + (no of nickles)(0.05) + (no of quarters)(0.25) = 7.00
d*(0.10) + n*(0.05) + q(0.25) = 7.00
usually written
0.10d + 0.05n + 0.25q = 7.00
Use the two equations q = n - 8 , d = 3n
and substitute (n-8) for q , and (3n) for d
0.10(3n) + 0.05n + 0.25(n - 8) = 7.00
0.30n + 0.05n + 0.25n - 2.00 = 7.00
add 2.00 to each side
0.30n + 0.05n + 0.25n = 9.00
0.60n = 9.00
multiply each side by 100
60n = 900
divide each side by 60
n = 15
d = 3n = 3(15) = 45
q = n - 8 = 15 - 8 = 7
Let's check
15*(0.05) + 45(0.10) + 7(0.25) ?= 7.00
0.75 + 4.50 + 1.75 = 7.00 which checks out