Question

You have 35 coins, consisting of nickels, dimes, and quarters. The value of the coins is $4.15. You also know that you have twice as many dimes as quarters. Find the number of each type of coin.

Answer 1

we know,
nickel = $0.05
dimes = $0.10
quarter = $0.25

Let number of quarters is x
so, number of dimes = 2x
and then number of nickels = 35 - (x + 2x) = 35 - 3x

now, total amount = $4.15

number of nickels × $0.05 + number of dimes × $0.10 + number of quarters × $0.25 = $4.15

(35 - 3x) × 0.05 + 2x × 0.10 + x × 0.25 = 4.15

(35 - 3x) × 5 + 2x × 10 + x × 25 = 415

175 - 15x + 20x + 25x = 415

30x = 415 - 175 = 240

x = 8

number of quarters = 8
number of dimes = 16
number of nickels = 35 - 16 - 8 = 11