Nicole has a collection of 29 nickels and dimes worth $2.30. How many of each does she have?

17 dimes

12 nickels

add up the coins, and add up the values:

n+d = 29
5n+10d = 230

Now just solve for n and d.

Thanks

To solve this problem, we can set up a system of equations based on the given information.

Let's assume that Nicole has x nickels and y dimes.

Since the total number of coins is 29, we can write the first equation as:
x + y = 29

Now, let's calculate the total value of the coins. Since a nickel is worth 5 cents and a dime is worth 10 cents, the total value in cents can be written as:
5x + 10y = 230

To eliminate the need to work with cents, we can divide the second equation by 5 to get:
x + 2y = 46

Now, we have a system of equations:
x + y = 29
x + 2y = 46

We can solve this system of equations using the method of substitution or elimination. Let's use the method of substitution here:

1. Solve the first equation for x: x = 29 - y
2. Substitute this value of x into the second equation: (29 - y) + 2y = 46
3. Simplify and solve for y: 29 + y = 46
y = 46 - 29
y = 17

Now that we have the value of y, we can substitute it back into the first equation to find the value of x:
x + 17 = 29
x = 29 - 17
x = 12

Therefore, Nicole has 12 nickels and 17 dimes.