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.