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

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

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x