Final answer:
Kiran has 20 nickels and 7 quarters in his pocket.
Step-by-step explanation:
To find out how many nickels and quarters Kiran has in his pocket, we can set up a system of equations based on the given information. Let's say the number of nickels is 'n' and the number of quarters is 'q'. We know that the total value of the coins is $2.75. Since a nickel is worth 5 cents and a quarter is worth 25 cents, we can write the following equations:
5n + 25q = 275 (equation 1) [since $2.75 is equal to 275 cents]
n + q = 27 (equation 2) [since Kiran has 27 nickels and quarters]
We can now apply the system of equations method to solve these equations. Multiplying equation 2 by 5 gives us 5n + 5q = 135. Subtracting equation 1 from this equation eliminates the 'n' term and gives us:
5q - 25q + 5n - 5n = 135 - 275
-20q = -140
We can solve this equation by dividing both sides by -20:
q = (-140)/(-20) = 7
Substituting this value of 'q' back into equation 2 gives us:
n + 7 = 27
n = 27 - 7 = 20
Therefore, Kiran has 20 nickels and 7 quarters in his pocket. Option a) is the correct answer.