You found $6.60 on the ground at school, all in nickels, dimes, and quarters. you have twice as many quarters as dimes and 42 coins in all. howmany of each type of coin do you have

Let the number of nickels found be n, the number of dimes be d and the number of quarters be q.

i) "you have twice as many quarters as dimes and 42 coins in all."

means that 2d=q, and n+d+q=42

we can reduce the number of unknowns by substituting q with 2d:

n+d+q=42
n+d+2d=42
n+3d=42

We can write all n, d and q in terms of d as follows:

there are n=42-3d nickels, d dimes and q=2d quarters.

ii) In total there are $6.60 dollars,

1 nickel     =  5 cent   =  $0.05
1 dime      =  10 cent  =  $0.1
1 quarter   =  25 cent  = $0.25 

thus

(42-3d)*0.05 + d*0.1 +2d*0.25= $6.60

2.1 - 0.15d+0.1d+0.5d=6.60

2.1+0.45d=6.6

0.45d=6.6-2.1=4.5

d=4.5/0.45=10

iii)

so, there are 10 dimes, 2d=2*10=20 quarters and 42-3d=42-3*10=12 nickels.

10 dimes, 20 quarters, 12 nickels

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