Let the number of nickel coins be n, the number of quarter coins be q and the number of dimes be d.
We know that 1 nickel= $0.05, 1 dime= $0.1 and 1 quarter= $0.25,
We found $6.60 means that : i) 0.05n+0.1d+0.25q=6.60
we have 42 coins in all mean: ii) n+d+q=42
we have twice as many quarters as dimes mean that iii) q=2d
using the last relation we can reduce the number of unknowns by writing all q's in terms of d's as follows:
i) 0.05n+0.1d+0.25q=6.60
ii) n+d+q=42
substitute q with 2d:
i) 0.05n+0.1d+0.25(2d)=6.60
ii) n+d+(2d)=42
i) 0.05n+0.1d+0.5d=6.60
ii) n+d+2d=42
i) 0.05n+0.6d=6.60
ii) n+3d=42
multiply the second equation by -0.2, to eliminate the d's:
i) 0.05n+0.6d=6.60
ii) -0.2n-0.6d=-8.4
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i+ii)
-0.2n+0.05n=6.60-8.4
-0.15n=-1.8
n=-1.8/(-0.15)=12
substitute in i):
0.05n+0.6d=6.60
0.05*12+0.6d=6.60
0.6+0.6d=6.60
0.6d=6.0
d=10
finally, from equation n+d+q=42:
12+10+q=42
22+q=42
q=42-22=20
Answer: # nickels=12, # dimes=10, # quarters=20