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We are given:

(1) 5n + 10d = 385; and

(2) n + d = 54.

From this, we may conclude:

(3) n + 2d = 77; {divide (1) by 5}

(4) d = 23; and {subtract (2) from (3)}

(5) n = 31. {subtract (4) from (2)}

Thus, there are 31 nickels, which answers your question.

Checking: we may see that 31 nickels make $1.55; and 23 dimes make $2.30. Thus, their total value is $3.85, and the total number of coins is 54, as you have specified.

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Q: A person has 54 coins all nickels and dimes worth 3.85 How many nickels are there?
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