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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

Answer :

jigglypuff314
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

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