Question

Robin has a collection of nickels, dimes, and quarters worth $63.50. she has 30 more dimes than nickels and twice as many quarters as dimes. how many coins of each kind does she have?

Answer 1

The first thing we must do is define variables:

x: number of nickels

y: number of dimes

z: number of quarters

We write the system of equations:

0.05x + 0.1y + 0.25z = 63.50

y = x + 30

z = 2y

Solving the system by substitution we have:

0.05x + 0.1 (x + 30) + 0.25 (2 (x + 30)) = 63.50

0.05x + 0.1x + 3 + 0.5x + 15 = 63.50

0.65x = 63.50 - 18

x = 45.5 / 0.65

x = 70

Then, the value of z and y is:

y = x + 30

y = 70 + 30

y = 100

On the other hand:

z = 2y

z = 2 (100)

z = 200

Answer:

70 nickels

100 dimes

200 quarters