Joseph has $1.45 worth of nickels and dimes. He has a total of 17 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Joseph has.
Let x be the number of nickels Joseph has.
The number of dimes Joseph has is 17 - x.
The value of the nickels Joseph has is 0.05x.
The value of the dimes Joseph has is 0.10(17 - x) = 1.70 - 0.10x.
The total value that Joseph has is 1.45.
So, the equation is 0.05x + 1.70 - 0.10x = 1.45.
Subtracting 1.70 from both sides of the equation, we get -0.05x = -0.25.
Dividing both sides of the equation by -0.05, we get x = 5.
Joseph has 5 nickels.
Therefore, Joseph has 17 - 5 = <<17-5=12>>12 dimes. Answer: \boxed{12}.