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