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?

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

70 nickels

100 dimes

200 quarters

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