10% of Fabian's savings was $33 more than 30% of George's savings. After Fabian spent ¹₆ of his savings and George spent 40% of his savings, Fabian had $560 more than George. How much was Fabian's saving at first?

	George	Fabian
Before	10 u	30 u + 330
Change	- 4 u	- 5 u - 55
After	6 u	25 u + 275
Comparing George and Fabian in the end		560 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Fabian = ³₁₀ George + 33 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Fabian = 3x110x1 George + 33 
330 Fabian = 310 George + 33 

Simplify the fractions.
¹₃₀ Fabian = ¹₁₀ George + 11

Let ¹₁₀ George be 1 u.

George's savings at first = 10 u

¹₃₀ Fabian = ¹₁₀ George + 11
Let ¹₃₀ Fabian be 1 u + 11.

Fabian's savings at first
= 30 x (1 u + 11) 
= 30 u + 330

Savings that George spent
= 40% x 10 u
= ⁴⁰₁₀₀ x 10 u
= 4 u

Savings that Fabian spent 
= ¹₆ x (30 u + 330)
= 5 u + 55 

Fabian had $560 more than George in the end. If another $560 was given to George, the amount that each had in the end would be the same.

25 u + 275 = 6 u + 560 
25 u - 6 u = 560 - 275
19 u = 285

1 u = 285 ÷ 19 = 15

Savings that Fabian had at first
= 30 u + 330
= 30 x 15 + 330
= 450 + 330
= $780

Answer(s): $780