Question 901494: A jar contains pennies, nickels, dimes and quarters. There are 3 times as many pennies as dimes, half as many nickels as quarters, and 4 times as many dimes as quarters. What is the minimum amount of money in the jar? If there are 175 coins, how much money is in the jar?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 3d=p,
4q=d,
q/2=n
p-3d=0
n-q/2=0
d-4q=0
p+n+d+q=175,
1,0,-3,0,0
0,1,0,-.5,0
0,0,1,-4,0
1,1,1,1,175
d = 40, n = 5, p = 120, q = 10,
x=p+5*n+10*d+25*q
x=795
1,0,-3,0,0
0,1,0,-.5,0
0,0,1,-4,0
1,1,1,1,175
divide row 1 by 1/1
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
1,1,1,1,175
add down (0/1) *row 1 to row 2
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
1,1,1,1,175
add down (0/1) *row 1 to row 3
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
1,1,1,1,175
add down (-1/1) *row 1 to row 4
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
0,1,4,1,175
divide row 2 by 1/1
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
0,1,4,1,175
add down (0/1) *row 2 to row 3
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
0,1,4,1,175
add down (-1/1) *row 2 to row 4
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
0,0,4,1.5/1,175
divide row 3 by 1/1
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
0,0,4,1.5/1,175
add down (-4/1) *row 3 to row 4
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
0,0,0,17.5/1,175
divide row 4 by 17.5/1
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,-4,0
0,0,0,1,10
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (4/1) *row 4 to row 3
1,0,-3,0,0
0,1,0,-0.5/1,0
0,0,1,0,40
0,0,0,1,10
add up (0.5/1) *row 4 to row 2
1,0,-3,0,0
0,1,0,0,5
0,0,1,0,40
0,0,0,1,10
add up (0/1) *row 4 to row 1
1,0,-3,0,0
0,1,0,0,5
0,0,1,0,40
0,0,0,1,10
add up (0/1) *row 3 to row 2
1,0,-3,0,0
0,1,0,0,5
0,0,1,0,40
0,0,0,1,10
add up (3/1) *row 3 to row 1
1,0,0,0,120
0,1,0,0,5
0,0,1,0,40
0,0,0,1,10
add up (0/1) *row 2 to row 1
1,0,0,0,120
0,1,0,0,5
0,0,1,0,40
0,0,0,1,10
final
1,0,0,0,120
0,1,0,0,5
0,0,1,0,40
0,0,0,1,10
1,0,0,0,120
0,1,0,0,5
0,0,1,0,40
0,0,0,1,10
"120","5","40","10"
(120,5,40,10)
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