1 nickle = 5 cents

1 quarter = 25 cents

Let

n = the number of nickles, n>=0

q = the number of quarter, q>=0

Ten nickles and quarters have a total of $1.70 = 170 cents:

n + q = 10

5n + 25q = 170

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click here to see the system of equations solved for n and q

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n = 4 nickles

q = 6 quarters

There are 4 nickles and 6 quarters.