Derrick has a total of 9 nickels and quarters in his pocket. The total amount of money he has in coins is $1.45. How many nickels and how many quarters does Derrick have? A. 3 nickels and 6 quarters B. 6 nickels and 3 quarters C. 4 nickels and 5 quarters D. 5 nickels and 4 quarters

Answer: 4 nickels and 5 quarters

Option C. 4 nickels and 5 quarters

Step-by-step explanation:

let the number of nickels = x, and the number of quarters = y

Derrick has a total of 9 nickels and quarters in his pocket

So, x + y = 9

∴ y = 9 - x ⇒ (1)

1 nickel = 5 cent = $0.05

1 quarter = 25 cent = $0.25

The total amount of money he has in coins is $1.45

So, 0.05 x + 0.25 y = 1.45

Multiply the both sides by 100

∴ 5x + 25y = 145 ⇒ (2)

Substitute with y from (1) at (2)

∴ 5x + 25 (9-x) = 145

Solve for x

5x + 225 - 25x = 145

-20x = 145 - 225 = - 80

x = - 80/-20 = 4

Substitute with x at (1)

y = 9 - 4 = 5

So, The number of nickels = 4, and the number of quarters = 5

The answer is option C. 4 nickels and 5 quarters