Question 890347: Shelly has $4.60 worth of quarters, dimes and nickels. She has one more nickel than twice the number of quarters and six more dimes than nickels. Write a system of equations using 3 variables to determine how many of each coin Shelly has.
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! n+6=d
2q+1=n
25q+10d+5n=460
1d-1n+0q=6
0d+1n-2q=1
10d+5n+25q=460
1,-1,0,6
0,1,-2,1
10,5,25,460
1,-1,0,6
0,1,-2,1
10,5,25,460
add down (0/1) *row 1 to row 2
1,-1,0,6
0,1,-2,1
10,5,25,460
add down (-10/1) *row 1 to row 3
1,-1,0,6
0,1,-2,1
0,15,25,400
divide row 2 by 1/1
1,-1,0,6
0,1,-2,1
0,15,25,400
add down (-15/1) *row 2 to row 3
1,-1,0,6
0,1,-2,1
0,0,55,385
divide row 3 by 55/1
1,-1,0,6
0,1,-2,1
0,0,1,7
We now have the value for the last variable.
We will work our way up and get the other solutions.
add up (2/1) *row 3 to row 2
1,-1,0,6
0,1,0,15
0,0,1,7
add up (0/1) *row 3 to row 1
1,-1,0,6
0,1,0,15
0,0,1,7
add up (1/1) *row 2 to row 1
1,0,0,21
0,1,0,15
0,0,1,7
final
1,0,0,21 dimes
0,1,0,15 nickels
0,0,1,7 quarters
210+075+175=460
|
|
|
