First off all, I think there is a mistyping.

It should be C= 3n + 20

Anyways you can simply take this approach.

1) For break even

C = R.

i.e

3n + 20 = 5n + 10

Solve for n.

n = 5

2) for profit of $100]

R - C = 100

(5n + 10) - (3n + 20) = 100

Solve for n

n = 55

Feel free to ask if you have any further doubts.