Problema Solution
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 provided by our tutors
1 nickle = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
Let
n = the number of nickels, n>0, n is integer
d = the number of dimes, d>0, d is integer
q = the number of quarters, q>0, q is integer
She has $4.65 = 465 cents altogether:
5n + 10d + 25q = 465
She has three more quarters than dimes
q = 3 + d
and twice as many nickels as quarters
n = 2q
We have the following system of equations:
5n + 10d + 25q = 465
q = 3 + d
n = 2q
........
........
n = 22 nickles
d = 8 dimes
q = 11 quarters
Rachna has 11 quarters.