Rachna has nickels, dimes, and quarters in her piggy bank. she has $4.65 altogether. she has three more quarters than dimes and twice as many nickels as quarters. how many quarters does rachna have?

a.8
b.11
c.22
d.41

The value of the coin times the number of coins equals the total value
so
0.05n + 0.10d + 0.25q = 4.65

the we are given that there are "three more quarters than dimes"
this translates to
q = d + 3
or
d = q - 3

then we are also given that there are "twice as many nickels as quarters"
this translates to
n = 2q

we plug d = q - 3 and n=2q
into the first equation and solve for q
0.05(2q) + 0.10(q-3) + 0.25q = 4.65

we distribute/multiply
0.10q + 0.10q - 0.30 + 0.25q = 4.65

then add like terms
0.45q - 0.30 = 4.65

then add 0.30 to both sides
0.45q = 4.95

then divide both sides by 0.45
and we get
q = 4.95/0.45 = 11

therefore there are 11 quarters