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?

Answer 1

11*.25=2.75+(22*.05)=3.85+(8*.1)=4.65
She has 11 quarters.

Answer 2

11 quarters.

Explanation:

Let Rachna has n nickels, d dimes and q quarters in her piggy bank.

"She has $4.65 altogether".

0.05n + 0.10d + 0.25q = 4.65

By diving this equation by 0.05

n + 2d + 5q = 93 ---------(1)

"She has three more quarters than dimes"

q = d + 3

d = q - 3 -------(2)

" She has twice as many nickels as quarters"

n = 2q --------(3)

Now we replace the values of d from equation 2 to eqaution 1

n + 2(q - 3) + 5q = 93

n + 2q - 6 + 5q = 93

n + 7q = 93 + 6

n + 7q = 99 ------(4)

By replacing n = 2q in equation 4 from equation 3

2q + 7q = 99

9q = 99

q = 11

Therefore, there are 11 quarters in the piggy bank.