Can someone explain the solution to this data sufficiency problem?

Rasheed bought two kinds of candy bars, chocolate and toffee, that came in packages of 2 bars each. He handed out 2/3 of the chocolate bars and 3/5 of the toffee bars. How many packages of chocolate bars did Rasheed buy?

1. Rasheed bought 1 fewer package of chocolate bars than toffee bars
2. Rasheed handed out the same number of each kind of candy bar

since both types of bars come 2 to a box, we can rephrase the question to just this: how many chocolate bars did he buy? (this works because the answer is just going to be double the number of packages; since it's data sufficiency, there's no good reason to waste the time doing the extra step).

so, in other words, we can ignore 'packages' and think in terms of bars instead.

--

(1)
rasheed bought 2 fewer chocolate bars than toffee bars.
so chocolate bars = x (this is what we want to find)
and toffee bars = x + 2
all we know is:
he hands out (2x/3) chocolate bars and (3x/5) toffee bars
INSUFFICIENT

(2) if c = # of chocolate bars and t = # of toffee bars, we know 2c/3 = 3t/5, which cross-multiplies to 10c = 9t.
this means that the ratio c : t is 9 : 10, but we have no idea what the actual numbers in the ratio are.
INSUFFICIENT

together:
taking both statements together, we have 10(x) = 9(x + 2), or (x) : (x + 2) = 9 : 10.
this is an equation with a unique solution.
SUFFICIENT (note that there is no need to solve; simply noting that there is 1 solution is good enough)

answer = c