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

For this case we have the following variables:

x: number of nickels

y: number of dimes

z: number of quarters

We now write the system of equations that models the problem:

`0.05x + 0.1y + 0.25z = 4.65  z = y + 3  x = 2z`

Rewriting the equations as a function of z we have:

`0.05 (2z) + 0.1 (z-3) + 0.25z = 4.65`

From here, we clear the value of z:

`0.1z + 0.1z - 0.3 + 0.25z = 4.65  0.1z + 0.1z + 0.25z = 4.65 + 0.3  0.1z + 0.1z + 0.25z = 4.65 + 0.3  0.45z = 4.95`

`z = (4.95)/(0.45)  z = 11`

Answer:

The number of quarters that Rachna has is:

B. 11

Answer 2

we can translate the given statements into algebraic expressions. In this case,

0.05x + 0.10y + 0.25z = 4.65z = 3 + yx = 2 z
solving these linear equations simultaneously, x = 22y = 8z= 11hence the answer is B. 11