Question 201379
I believe your answer is going to be

15 nickels (75 cents)
8 dimes     (80 cents)
2 quarters   (50 cents)

that adds up to be $2.05

here's how I did it.

let n = number of nickels
let d = number of dimes
let q = number of quarters

n + d + q = 25 (number of coins in total)

number of dimes is 4 times the number of quarters (n = 4d)

total value of coins is $2.05

$.05 * n + $.10 * d + $.25 * q = $2.05

take away the dollar sign and multiply both sides of the equation by 100 and you get

5n + 10d + 25q = 205

since d = 4q you can substitute to get

5n + 40q + 25q = 205

since n + d + q = 25 you can substitute 4q for d again to get

n + 5q = 25

solve for n to get

n = 25 - 5q

multiply both sides of the equation by 5 to get

5n = 125 - 25q

substitute in the equation 5n + 40q + 25q = 205 to get

125 - 25q + 40q + 25q = 205

simplify the left side of the equation to get

125 + 40q = 205

solve for q to get

40q = 80

q = 2

since d = 4q, then d = 8

since n + d + q = 25, then n = 15

your answer is

n = 15
d = 8
q = 2

as shown above.