Sarah has a collection of nickels, dimes, and pennies worth $5.06. she has five times as many nickels as pennies; and she has two times as many dimes as pennies. how many coins of each kind does she have?

11 pennies (:
506cents=x +5*5*x+2*10*x
5*x = nickels
10*x=dimes
506=46x
506/46=x
X=11

The best way to even begin solving this problem, is to organize:
N-Nickels
P-Pennies
D-Dimes
N=0.05
P=0.01
D=0.10
Total= $5.06
We begin to write the equation as :
0.01p+0.05(5p)+0.10(2p)=$5.06
p represents pennies so the 5p represents the fact that nickels equals 5 times the amount of pennies and the 2p represents the fact that dimes equals 2 times the amount of pennies.
Multiply to get rid of the parenthesis.
0.01p+0.25p+0.20p=$5.06
Add up all the numbers on the left side of the equal sign: 
0.46p=$5.06
Divide both side by 0.46 to isolate p.
p=11.
Therefore there are 11 pennies.
Nickels is 5 times the amount of pennies so:
5*11=55 nickels.
Dimes is 2 times the amount of pennies so:
2*11=22 dimes.
55 nickels is equal to $2.75
22 dimes is equal to $2.20
11 pennies is equal to $0.11
Add them all up and you get $5.06.

Hope this helps! (: