How many nickels and dimes are there in a pile of 55 coins that is worth $3.90?

Finding the Number of Nickels and Dimes

To solve the problem of a pile of 55 coins made up of nickels and dimes worth $3.90, we can use a system of equations.

Define Variables

• Let n be the number of nickels.
• Let d be the number of dimes.

Set Up the Equations

We can create two equations based on the information given:

1. The total number of coins: n + d = 55
2. The total value of the coins in cents: 5n + 10d = 390

Solving the Equations

We can solve these equations step by step.

Step 1: Solve for one variable

From the first equation, we can express d in terms of n:

d = 55 - n

Step 2: Substitute into the second equation

Now we substitute d into the second equation:

5n + 10(55 - n) = 390

Step 3: Simplify the equation

Distributing the 10:

5n + 550 - 10n = 390

This simplifies to:

-5n + 550 = 390

Step 4: Isolate n

Subtract 550 from both sides:

-5n = 390 - 550

-5n = -160

Now divide by -5:

n = 32

Step 5: Find d

Using the value of n to find d:

d = 55 - n = 55 - 32 = 23

Conclusion

So, there are 32 nickels and 23 dimes in the pile of coins. To check our work:

• Value from nickels: 32 x 5 = 160 cents
• Value from dimes: 23 x 10 = 230 cents
• Total value: 160 + 230 = 390 cents, which is $3.90

This confirms our solution is correct!