Question

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 1

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

`0.05n + 0.10d + 0.25q = 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

`q = d + 3`
or

`d = q - 3`

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

`n = 2q`

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

`0.05(2q) + 0.10(q - 3) + 0.25q = 4.65`

then we distribute and start trying to solve for
`q`

`0.10q + 0.10q - 0.30 + 0.25 = 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

`q = (4.95)/(0.45) = 11`

therefore our answer is B) 11 quarters