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A collection of coins consisting of nickels dimes and quarters amount to 7.20. There are six more dimes than nickels and six more quarters than dimes. Find the number of each kind of coin.

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pedrocarratore

Answer:

9 nickles

15 dimes

21 quarters

Step-by-step explanation:

Number of nickels = N

Number of dimes = D

Number of quarters = Q

The following system can be modeled based of the given information:

[tex]0.05N+0.10D+0.25Q=7.20\\D=N+6\\Q=D+6[/tex]

Solving the system:

[tex]D=N+6\\Q=N+6+6=N+12\\0.05N+0.10*(N+6)+0.25*(N+12)=7.20\\0.4N=7.20-0.6-3\\N=9\\D=9+6=15\\Q=15+6=21[/tex]

The collection consists of 9 nickels, 15 dimes and 21 quarters.

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