Both of your translations are correct.

When you're not sure how to translate, plugging in numbers that you understand is often a good way to figure out where to place the variables.

For example:

"There are 3 times as many people aged twenty-one or under as there are people over twenty one."

or, to simplify:

"There are 3 times as many X as Y."

OK.. so if we had 6 Xs, and there are 3 times as many X as Y, we should have 2 Ys.

So if X=6 and Y=2, the relationship is:

X = 3Y

Similarly for the second example:

"1/3 as many violets as carnation"

If we translated that as:

(1/3)V = C and picked numbers, we'd get something like V=9 and C=3. But that's not 1/3 as many violets as carnations, that's three times as many violets as carnations... clearly we've gotten the variables backwards.

(1/3)C = V, that would be C=9 and V=3... yup, that's 1/3 as many violets as carnations, so it must be the correc translation.

All I understand is,

A : people aged twenty-one
C : people aged under twenty-one
B : people aged over twenty one

A: 3x
C: 3X
B: x

C/(A+B+C) or A/(A+B+C)
C=A, then C/(A+B+C) = A/(A+B+C)

But what if it said, there are 3 times as many
people aged twenty-one and under as there are people
over twenty-one, then the answer...?(not actually asking the answer)