Robin split a total of $24,000 between 2 investments

Robin split a total of $24,000 between 2 investments, X and Y. If investment earns 7% simple annual interest, how much of that total did Robin put into investment Y?
1. Each investment earns the same dollar amount of the interest annually.
2. Investment X earns 5 percent simple annual interest.

ok:
first, find expressions for the interest on each of the two accounts:
interest on x = 0.07x
interest on y = (rate)(24000 - x)
(1) alone:
0.07x = (rate)(24000 - x)
this is one linear equation, with two unknowns, so it can't be solved uniquely.
insufficient
(2) alone:
interest on x = 0.07x
interest on y = 0.05(24000 - x)
but there's no equation relating these two things
insufficient
together:
0.07x = 0.05(24000 - x)
linear equation in one variable --> can be solved uniquely
sufficient
answer = c