A pile of 55 nickels and dimes is worth $3.90. What is the number of nickels and the number of dimes?
Let's assume that the number of nickels in the pile is "x" and the number of dimes is "y."
Since we know that there are a total of 55 nickels and dimes, we can write the following equation:
x + y = 55
We are also told that the pile is worth $3.90. Since each nickel is worth 5 cents and each dime is worth 10 cents, we can write the following equation:
0.05x + 0.10y = 3.90
Now we can use the first equation to solve for one of the variables in terms of the other:
x = 55 - y
We can substitute this expression for x into the second equation and simplify:
0.05(55 - y) + 0.10y = 3.90
2.75 - 0.05y + 0.10y = 3.90
0.05y = 1.15
y = 23
So we have found that there are 23 dimes in the pile. To find the number of nickels, we can substitute y=23 back into either of the previous equations:
x + 23 = 55
x = 32
Therefore, there are 32 nickels in the pile.