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?
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 [tex] 0.05n + 0.10d + 0.25q = 4.65 [/tex] 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 [tex] q = d + 3 [/tex] or [tex] d = q - 3 [/tex]
we are also told that there are "twice as many nickels as quarters" this translates to [tex] n = 2q [/tex]
to solve for quarters, we plug in d (in terms of q) and n (in terms of q) into the first equation we created. [tex] 0.05(2q) + 0.10(q - 3) + 0.25q = 4.65 [/tex]
then we distribute and start trying to solve for [tex]q[/tex] [tex] 0.10q + 0.10q - 0.30 + 0.25 = 4.65 [/tex]
then add like terms [tex] 0.45q - 0.30 = 4.65 [/tex]
then add 0.30 to both sides [tex] 0.45q = 4.95 [/tex]
then divide both sides by 0.45 [tex] q = \frac{4.95}{0.45} = 11 [/tex]
