Kiran has 27 nickels and quarters in his pocket, with a total value of $2.75. We need to determine the number of nickels and quarters Kiran has. We will set up a system of equations to represent the given information and then solve for the number of nickels ($n$) and the number of quarters ($q$).

1. Problem Description

Kiran has 27 nickels and quarters in his pocket, with a total value of $2.

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5. We need to determine the number of nickels and quarters Kiran has. We will set up a system of equations to represent the given information and then solve for the number of nickels ($n$) and the number of quarters ($q$).

2. Solution Steps

a. We are given that Kiran has a total of 27 nickels and quarters. This can be represented by the equation:

$n + q = 27$

The value of $n$ nickels is $0.05n$ dollars, and the value of $q$ quarters is $0.25q$ dollars. The total value of the coins is $2.

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5. This gives us the equation:

$0.05n + 0.25q = 2.75$

Therefore, the system of equations is:

$n + q = 27$

$0.05n + 0.25q = 2.75$

b. We can solve the system of equations to find the values of $n$ and $q$. First, we can solve the first equation for $n$:

$n = 27 - q$

Now, substitute this expression for $n$ into the second equation:

$0.05(27 - q) + 0.25q = 2.75$

$1.35 - 0.05q + 0.25q = 2.75$

$0.20q = 2.75 - 1.35$

$0.20q = 1.40$

$q = \frac{1.40}{0.20}$

$q = 7$

Now, substitute the value of $q$ back into the equation $n = 27 - q$:

$n = 27 - 7$

$n = 20$

So, Kiran has 20 nickels and 7 quarters.

3. Final Answer

Kiran has 20 nickels and 7 quarters.