Question 371773: Kim has a bunch of coins which are all nickels, dimes and quarters. Her dimes and her quaters add up to $7.85. Her quaters and her nickels add up to $6.35. Her nickels and her dimes add up to $4.70. Write equations to help figure out how many nickels, dimes and quarters she has. Then solve for each variable.
Answer by Math-Help(7)   (Show Source):
You can put this solution on YOUR website! nickels = .05
dimes = .10
quarters = .25
Let x = number of nickels
Let y = number of dimes
Let z = number of quarters
.10y + .25z = 7.85
.05x + .25z = 6.35
.05x + .10y = 4.70
Using the elimination method:
.10y + .25z = 7.85
-(.05x + .25z = 6.35)
Thus -.05x + .10y = 1.50
Now add:
-.05x + .10y = 1.50
.05x + .10y = 4.70
Thus .20y = 6.20
y = 31
Substitute y into .05x + .10y = 4.70
.05x + .10(31) = 4.70
.05x + 3.10 = 4.70
.05x = 1.60
x = 33
Substitute x into .05x + .25z = 6.35
.05(33) + .25z = 6.35
1.60 + .25z = 6.35
.25z = 4.75
z = 19
Therefore, x=33 (nickels), y=31 (dimes), z=19 (quarters)
Double Check:
.10y + .25z = 7.85
.10(31) + .25(19) =?= 7.85
3.10 + 4.75 =?= 7.85
7.85 = 7.85 Correct!
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