Dimes All

A student finds $1.05 in dimes, nickels and pennies. If there are 17 coins in all, how many coins of each type?

A student finds $1.05 in dimes, nickels
and pennies. If there are 17 coins in all, how many coins of each
type can he have?
This is what i got..
0.10 x + 0.05 y + 0.01 z = 1.05
x + y + z = 17 ,
but i don’t what to do next
please explain how you do it ,ty!

There are actually infinitely many solutions, except that in the real world, the quantity of each coin must be an integer, and non-negative.

I would attack this by starting with all dimes to see how close I could get. 10 dimes is a dollar. Ok, add 5 pennies for $1.05. That makes 15 coins. Every time I trade one dime for 2 nickels, I get one more coin, but keep the total the same. So I must do this twice. And there’s the answer.

But there’s another answer. Since the total amount ends in .05, there must be 0 pennies, or 5 pennies, or 10 pennies, or 15 pennies. Can’t be 20 pennies, because there are only 17 coins. It can’t even be 10 pennies, because then even if all the rest of the coins are dimes, that’s still only 80 cents. Ok, let’s look at 0 pennies. You will find that there’s a solution in dimes and nickels that satisfies this case. However, the text says that the student found dimes, nickels, and pennies, so that means there must be some of each coin, and 0 is not a fair number.

MF Doom-Rhymes Like Dimes