SOLUTION: While cleaning out the closet, John found a box of coins. The box contained nickels, dimes, and quarters. He added up the change and found that there were 85 coins totaling $6.25

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Question 157473: While cleaning out the closet, John found a box of coins. The box contained nickels, dimes, and quarters. He added up the change and found that there were 85 coins totaling $6.25 in the box. If there were 3 times as many nickels as dimes, how many quarters were there?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=number of nickels
And let y=number of dimes
And z=number of quarters
Now we are told that:
x+y+z=85---------------------------------eq1
and
0.05x+0.10y+0.25z=6.25--------------------eq2
and
x=3y--------------------------------------eq3
Substitute eq3 into eq1 and eq2
3y+y+z=85 or
4y+z=85---------------------------------------eq1a
and
0.15y+0.10y+0.25z=6.25 or
0.25y+0.25z=6.25 divide each term by 0.25
y+z=25---------------------------------------------eq2a
subtract eq2a from eq1a:
3y=60 divide each side by 3
y=20--------------------------------number of dimes
substitute y=20 into eq3
x=3*20=60--------------------------number of nickels
substitute y=20 and x=60 into eq1
80+z=85
z=5-----------------------------NUMBER OF QUARTERS-----ANS
CK
0.05*60+0.10*20+0.25*5=6.25
3.00+2.00+1.25=6.25
6.25=6.25
and
20+60+5=85
85=85
Hope this helps--ptaylor