Danny     [u][u][u][u]

Ethan      [u][u][u]

Caleb       [837-7u]

After Danny and Caleb spent 1/3 of their money, $648 is left

(1/3)(4u) + (1/3)(837-7u) = 837-648 = 189           ( x 3 on both sides)

4u + 837 – 7u =  567

3u = 270

u =90

Hence at first Caleb has 837-7(90) = $207

Caleb and Danny spent 837 - 648 = 189. That is 1/3 of their money.
So Caleb and Danny had 3 x 189 = 567 altogether.
Thus Ethan had 837 - 567 = 270.
But Danny:Ethan = 4:3, so that means Danny had 4 x 270/3 = 360.
Answer: Caleb had 837 - 270 - 360 = $207 at first.