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

From all this information we can come up with a few equations to work with...

first we have that the worth of each coin times the number of those coins all added together equals 4.65

here I have n = nickels, d = dimes, and q = quaters

then we are told that there are "three more quarters than dimes"
which translates to the equation

or


we are also told that there are "twice as many nickels as quarters"
this translates to


to solve for quarters, we plug in d (in terms of q) and n (in terms of q) into the first equation we created.


then we distribute and start trying to solve for


then add like terms


then add 0.30 to both sides


then divide both sides by 0.45


therefore our answer is B) 11 quarters