Question

A collection of nickels, dimes, and quarters amounts to $12.35. If there are 169 coins in all and there are twice as many dimes as there are quarters, find the number of nickels.

Answer 1

Let the numbers of the coins be n, d and q.

n+d+q=169, 5n+10d+25q=1235 cents.

d=2q, so 5n+20q+25q=1235.

So 5n=1235-45q and n=247-9q, so 9q=247-n.

Also n+2q+q=169, n=169-3q or 3n=507-9q=507-(247-n).

Therefore, 3n=507-247+n, 2n=260 so n=130. (9q=247-130=117 so q=13 and d=26).

There are 130 nickels.