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nickels dimes and quarters worth 57.50 she has 20 more dimes than nickels. twice as many quarters as dimes. how many of each?

Robin has a collection of nickels, dimes, and quarters worth $57.50. She has 20 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?

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Mikhail K. | Effective K-12 and college Math and Science TutorEffective K-12 and college Math and Scie...
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Let n be a number of nickels, d - dimes and q - quarters.
Then d=20+n and q=2d (*)
Since 25q+10d+5n=5750 -> 25(2d) + 10d + 5(d-20)=5750.
Simplifying, we get 65d-100=5750,  65d=5850, d = 90.
Substituting in (*) we get n=70, q=180.
Answer: Robin has 70 nickels, 90 dimes and 180 quarters.