Unit-part method

From the question, it can be deduced that they have the same number of marbles and stickers at first.

After losing 24 marbles, Deborah's number of marbles are 60% of her stickers.
60%→ 6/10 = 3/5

Deborah's marbles now = 3u
Deborah's stickers = 5u
Deborah's marbles at first = 3u + 24

After losing 16 stickers , Eddie's number of stickers are 1/3 of his marbles.

Eddie's stickers now = 1p
Eddie's marbles = 3p
Eddie's stickers at first = 1p + 16

Remember they each had the same number of stickers and marbles at first.

So,
3u + 24 = 3p
5u = 1p + 16

Make the number of u the same.

(3u + 24) x 5 = 3p
15u + 120 = 15p
So 15u = 15p - 120

5u x 3 = (1p + 16) x 3
15u = 3p + 48

Comparing the above,
15p - 120 = 3p + 48
12p = 168
1p = 14

Number of marbles Eddie has
= 3p = 3 x 14 = 42

Number of marbles Deborah bought
= 42 + 42 = 84

(or 42 x 2, since they have the same number of marbles after Deborah bought and gave half to Eddie)


Alternatively,

3u + 24 = 3p
So 1u + 8 = 1p

Remember that 5u = 1p + 16

But we also now know that 1u + 8 = 1p

So 1p + 16 = (1u + 8) + 16 = 1u + 24

And thus 1u + 24 = 5u
4u = 24
1u = 6

Then 1p = 1u + 8 = 6 + 8 = 14

Thanks for your detailed explanation.