Sarah has a collection of nickels, dimes, and quarters worth $15.10. she has 10 more dimes than nickels and twice as many quarters as dimes. how many coins of each kind does she have?

let x represent the number of nickels.

As she has 10 more dimes than nickels, the number of dimes is x + 10.

As she has twice as many quarters as dimes, the number of quarters is 2 (x + 10)

the total value is $15.10, so I get an equation:

0.05x + 0.1 * (x + 10) + 0.25*2 (x + 10) = 15.10

0.05x + 0.1x + 1 + 0.5x + 5 = 15.10

0.65x = 9.1

x = 14

x + 10 = 24

2 (x + 10) = 48

there are 14 nickes, 24 dimes and 48 quarters