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?

if the variable n represents the number of nickels, then which expressions represents the number of quarters?

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

(-0, -7) is your answer