Let x be the number of dimes and y be the number of nickels that Breck has. We know that he has 22 coins in total so
x + y = 22
We also know that the total value of the coins is $1.45, which is equivalent to 145 cents. Since dimes are worth 10 cents and nickels are worth 5 cents, we can write another equation:
10x + 5y = 145
We can simplify this equation by dividing both sides by 5:
2x + y = 29
Now we have two equations:
x + y = 22
2x + y = 29
We can solve for y by subtracting the first equation from the second equation:
2x + y - (x + y) = 29 - 22
x = 7
Now that we know x, we can substitute it back into either equation to solve for y:
x + y = 22
7 + y = 22
y = 15
Therefore, Breck has 7 dimes and 15 nickels.