If 120 gadgets cost $44, then, at the same price, 180 gadgets would cost what?

So far, so good. Now, the worst thing in the universe you could possibly do at this point is proceed to multiply 44 times 180. That's a disastrous move. Instead, CANCEL BEFORE YOU MULTIPLY!

That's an algebraic solution, for those who want one. Notice, even more elegant: 180 is 50% greater than 120, so the cost should be 50% greater than $44. Well, half of $44 is $22, and 44 + 22 = $66. If you see that, that's a very elegant way to think about this.