A collection of dimes and nickels is worth 3.30. if there are 42 coins in total how many of each kind of coin are there?

1 nickels = $0.05

1 dime = $0.1

let the number of nickels be x and that of dimes be y.

total number of coins is given by:

x+y=42

hence:

y=42-x ... i

total amount of cash will be:

0.05x+0.1y=3.30 ... ii

substituting i in ii we get:

0.05x+0.1 (42-x) = 3.30

0.05x+4.2-0.1x=3.3

-0.05x=-0.9

x=-0.9 / (-0.05)

x=18

hence the the number nickels is x=18, the number of dimes will be y=42-x=42-18=24