Let the number of nickles = N

Then....the number of dimes = 7N

And

No. of nickles * their value each + No. of dimes * their value each = total value

So we have

N(5) + 7N(10 ) = 300 simplify

5N + 70N = 300

75N = 300 divide both sides by 75

4 = N ⇒ [ 4 nickles ]