Kyle has 13 coins in his pocket that are either quarters or nickels. He has $2.05 in his pocket in coins.
Let q represent the number of quarters and n represent the number of nickels. The following system of equations represents this situation:
q+n=13
0.25q+0.05n=2.05
How many nickels and quarters does Kyle have?
1 q + 1 n = 13
1 q + .2n = 8.2
---------------subtract
.8 n = 4.8
so 6 nickels
67
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To determine the number of nickels and quarters Kyle has, we can solve the system of equations provided.
The first equation, q + n = 13, represents the total number of coins Kyle has. It states that the sum of the number of quarters (q) and nickels (n) is equal to 13.
The second equation, 0.25q + 0.05n = 2.05, represents the total value of the coins Kyle has. It states that the sum of 0.25 multiplied by the number of quarters (q) and 0.05 multiplied by the number of nickels (n) is equal to $2.05.
To solve this system of equations, we can use the method of substitution:
1. Solve the first equation for either q or n. Let's solve for n by subtracting q from both sides:
n = 13 - q
2. Substitute the expression for n in the second equation:
0.25q + 0.05(13 - q) = 2.05
3. Simplify and solve for q:
0.25q + 0.65 - 0.05q = 2.05
0.20q + 0.65 = 2.05
0.20q = 2.05 - 0.65
0.20q = 1.40
q = 1.40 / 0.20
q = 7
4. Substitute the value of q back into the first equation to find n:
7 + n = 13
n = 13 - 7
n = 6
Therefore, Kyle has 7 quarters and 6 nickels.