Answer:
9.9 quarters or Approximately ≈ 10
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 = $0.25
0.05n + 0.10d + 0.25q =$ 3.65.......Equation 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 coins........Equation 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 = 3.65.........Equation 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