Kyle has a total of 16 coins in his pocket. All the coins are nickels or quarters, and they have a total value of $2.20. How many nickels does Kyle have?

9 Nickels

X Nickels.

(16-X) Qtrs.

5x + 25(16-X) = 220 Cents. Solve for X.

Let's solve this problem step by step.

Step 1: Let's assume that Kyle has x nickels and y quarters.
- x represents the number of nickels.
- y represents the number of quarters.

Step 2: We know that Kyle has a total of 16 coins. Therefore, x + y = 16.

Step 3: We also know that the total value of all the coins is $2.20.
- The value of a nickel is $0.05, so the total value of nickels is 0.05x.
- The value of a quarter is $0.25, so the total value of quarters is 0.25y.

Therefore, we can write the second equation as 0.05x + 0.25y = 2.20.

Step 4: Now we have a system of two equations:
x + y = 16 (Equation 1)
0.05x + 0.25y = 2.20 (Equation 2)

We will solve this system of equations using substitution.

Step 5: Solve Equation 1 for x:
x = 16 - y

Step 6: Substitute x = 16 - y into Equation 2:
0.05(16 - y) + 0.25y = 2.20

Step 7: Simplify the equation:
0.8 - 0.05y + 0.25y = 2.20

Step 8: Combine like terms:
0.2y = 1.4

Step 9: Divide both sides of the equation by 0.2:
y = 7

Step 10: Substitute y = 7 back into Equation 1 to find x:
x + 7 = 16
x = 16 - 7
x = 9

Step 11: Therefore, Kyle has 9 nickels.

To determine the number of nickels Kyle has, we need to set up a system of equations based on the given information.

Let's assume the number of nickels Kyle has is represented by 'n', and the number of quarters is represented by 'q'.

From the first statement, we know that Kyle has a total of 16 coins. Therefore, we can write the equation:

n + q = 16 -- Equation 1

From the second statement, we know that the total value of the coins is $2.20. Since a nickel is worth $0.05 and a quarter is worth $0.25, we can write the equation for the total value:

0.05n + 0.25q = 2.20 -- Equation 2

To solve this system of equations, we can use the substitution or elimination method. Let's solve it using the substitution method:

From Equation 1, we have n = 16 - q. Substitute this value into Equation 2:

0.05(16 - q) + 0.25q = 2.20
0.80 - 0.05q + 0.25q = 2.20
0.20q = 2.20 - 0.80
0.20q = 1.40
q = 1.40 / 0.20
q = 7

Now that we know the number of quarters (q = 7), we can substitute this value back into Equation 1 to find the number of nickels:

n + 7 = 16
n = 16 - 7
n = 9

Therefore, Kyle has 9 nickels.