Question 901781: A jar contains 125 coins including only nickels dimes and quarters worth $21.90. There are twice as many nickels as dimes. How many of each type of coin is in the jar?
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! 5*n+10*d+25*q=2190
n+d+q=125
2*d=n
n-2*d=0
5,10,25,2190
1,1,1,125
1,-2,0,0
5,10,25,2190
1,1,1,125
1,-2,0,0
divide row 1 by 5
1,2,5,438
1,1,1,125
1,-2,0,0
add down (-1) *row 1 to row 2
1,2,5,438
0,-1,-4,-313
1,-2,0,0
add down (-1) *row 1 to row 3
1,2,5,438
0,-1,-4,-313
0,-4,-5,-438
divide row 2 by -1
1,2,5,438
0,1,4,313
0,-4,-5,-438
add down (4) *row 2 to row 3
1,2,5,438
0,1,4,313
0,0,11,814
divide row 3 by 11
1,2,5,438
0,1,4,313
0,0,1,74
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (-4) *row 3 to row 2
1,2,5,438
0,1,0,17
0,0,1,74
add up (-5) *row 3 to row 1
1,2,0,68
0,1,0,17
0,0,1,74
add up (-2) *row 2 to row 1
1,0,0,34
0,1,0,17
0,0,1,74
final
1,0,0,34
0,1,0,17
0,0,1,74
"34","17","74"
(34,17,74)
34n 17d 74q
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