SOLUTION: A person has 91 coins made up of pennies, nickels, dimes, and quarters. The total value of the coins is $6.25 and there are 4 times as many nickels as quarters. Additionally, the v

Question 901591: A person has 91 coins made up of pennies, nickels, dimes, and quarters. The total value of the coins is $6.25 and there are 4 times as many nickels as quarters. Additionally, the value in quarters is 12 times the value in pennies. How many of each type of coin does this person have? Let p, n, d, and q be the number of pennies, nickels, dimes, and quarters the person has respectively.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
4*q=n
25q=12*p
This hints that p=25 and q=12
then that n=48
48+12+25+d=91
d=6
p+5*n+10*d+25*q=625
12p-25q=0
n-4q=0
p+n+d+q=91

1,5,10,25,625
12,0,0,-25,0
1,1,1,1,91
0,1,0,-4,0
divide row 1 by 1
1,5,10,25,625
12,0,0,-25,0
1,1,1,1,91
0,1,0,-4,0
add down (-12) *row 1 to row 2
1,5,10,25,625
0,-60,-120,-325,-7500
1,1,1,1,91
0,1,0,-4,0
add down (-1) *row 1 to row 3
1,5,10,25,625
0,-60,-120,-325,-7500
0,-4,-9,-24,-534
0,1,0,-4,0
add down (0) *row 1 to row 4
1,5,10,25,625
0,-60,-120,-325,-7500
0,-4,-9,-24,-534
0,1,0,-4,0
divide row 2 by -60
1,5,10,25,625
0,1,2,-325/-60,125
0,-4,-9,-24,-534
0,1,0,-4,0
add down (4) *row 2 to row 3
1,5,10,25,625
0,1,2,65/12,125
0,0,-1,-28/12,-34
0,1,0,-4,0
add down (-1) *row 2 to row 4
1,5,10,25,625
0,1,2,65/12,125
0,0,-1,-7/3,-34
0,0,-2,-113/12,-125
divide row 3 by -1
1,5,10,25,625
0,1,2,65/12,125
0,0,1,-7/-3,34
0,0,-2,-113/12,-125
add down (2) *row 3 to row 4
1,5,10,25,625
0,1,2,65/12,125
0,0,1,7/3,34
0,0,0,-171/36,-57
divide row 4 by -19/4
1,5,10,25,625
0,1,2,65/12,125
0,0,1,7/3,34
0,0,0,1,12
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-7/3) *row 4 to row 3
1,5,10,25,625
0,1,2,65/12,125
0,0,1,0,6
0,0,0,1,12
add up (-65/12) *row 4 to row 2
1,5,10,25,625
0,1,2,0,60
0,0,1,0,6
0,0,0,1,12
add up (-25) *row 4 to row 1
1,5,10,0,325
0,1,2,0,60
0,0,1,0,6
0,0,0,1,12
add up (-2) *row 3 to row 2
1,5,10,0,325
0,1,0,0,48
0,0,1,0,6
0,0,0,1,12
add up (-10) *row 3 to row 1
1,5,0,0,265
0,1,0,0,48
0,0,1,0,6
0,0,0,1,12
add up (-5) *row 2 to row 1
1,0,0,0,25
0,1,0,0,48
0,0,1,0,6
0,0,0,1,12
final
1,0,0,0,25
0,1,0,0,48
0,0,1,0,6
0,0,0,1,12
"25","48","6","12"
(25,48,6,12)

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