A pile of 55 nickels and dimes is worth $3.90. Find the number of nickels and the number of dimes.
Let n be the number of nickels and d be the number of dimes. We know that n + d = 55 and 0.05n + 0.1d = 3.90. We will solve these equations simultaneously to get the value of n and d.
Solve the first equation for d: d = 55 - n
In the second equation, replace d with 55 - n: 0.05n + 0.1(55 - n) = 3.90
Expand and simplify: 0.05n + 5.5 - 0.1n = 3.90
Add 0.1n and subtract 5.5 from both sides to get: 0.05n = -1.6
Divide both sides by 0.05 to get: n = -1.6 / 0.05 = 32
Since d = 55 - n, d = 55 - 32 = 23
So, there are 32 nickels and 23 dimes.