Peggy had four times as many quarters as nickels. she had $2.10 in all. how many nickels and how many quarters did she have?

which of the following equations could be used to solve the problem?

Value of the coin times number of coins summed up equal total value
so since we have "$2.10 in all"...
0.05n + 0.25q = 2.10

and we are told that there are "four times as many quarters as nickels"
this translates to
q = 4n

0.05n + 0.25q = 2.10
and
q = 4n
are your two equations that could be used to solve this problem

if you would like to know how many nickels and how many quarters there are, plug in q = 4n into the first equation and get
0.05n + 0.25(4n) = 2.10

multiply
0.05n + 1n = 2.10

add like terms
1.05n = 2.10

divide both sides by 1.05
n = 2.10/1.05 = 2

then plug that back into
q = 4n
so
q = 4(2) = 8

therefore you have 
2 nickels
and
8 quarters