Mickey has a bag of 30 containing nickels, dimes, and quarters. The total value of the 30 coins is $3.65. There are twice as many nickels as there are dimes. Find the numbers of quarters

9.9 quarters or Approximately ≈ 10

Step-by-step explanation:

Let n = number of nickels

d =number of dimes

q = number of quarters

n + d + q = 30 coins Equation 1

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

0.05n + 0.10d + 0.25q =$ 3.65Equation 2

There are twice as many nickels as there are dimes.

Hence

n = 2d

n + d + q = 30 coins

2d + d + q = 30 coins

3d + q = 30 coinsEquation 3

3d = 30 - q

d= 30 - q/3

0.05n + 0.10d + 0.25q =$ 3.65

Since n = 2d

0.05(2d) + 0.10d + 0.25q = $3.65

0.10d + 0.10d + 0.25q = 3.65Equation 4

Substitute 30 - q/3 for d in Equation 4

0.10(30 - q/3) + 0.10(30 - q/3) + 0.25q = 3.65

= 3 - 0.10q/ 3 + 3 - 0.10q/3 + 0.25q

(3 - 0.10q) + (3 - 0.10q) + 3(0.25q)/ 3 = 3.65

Cross multiply

(3 - 0.10q) + (3 - 0.10q) + 3(0.25q) = 3 × 3.65

3- 0.10q+ 3 - 0.10q + 0.75q = 10.95

6 - 0.20q + 0.75q = 10.95

0.50q = 10.95 - 6

0.50q = 4.95

q = 4.95/0.50

q = 9.9 quarters

Therefore, the numbers of quarters is approximately ≈ 10 quarters

the answer is d. 75%