1 nickle = 5 cents = $0.05

1 dime = 10 cents = $0.1

1 quarter = 25 cents = $0.25

let

x = the number of nickles

y = the number of dimes

z = the number of quarters

a collection of nickels, dimes and quarters amount to $10.00

0.05x + 0.1y + 0.25*z = 10

there are 140 coins in all

x + y + z = 140

there are twice as many dimes as there are quarters

z = 2y

by solving the system of 3 equations

0.05x + 0.1y + 0.25*z = 10

x + y + z = 140

z = 2y

we find

x = 120 nickles

y = 20/3 dimes

z = 40/3 quarters

There are 120 nickles.