20% of Fabian's savings was $38 more than 40% of Zane's savings. After Fabian spent ¹₂ of his savings and Zane spent 40% of his savings, Fabian had $127 more than Zane. How much was Fabian's saving at first?

	Zane	Fabian
Before	5 u	10 u + 190
Change	- 2 u	- 5 u - 95
After	3 u	5 u + 95
Comparing Zane and Fabian in the end		127 more

20% = ²⁰₁₀₀ = ¹₅

40% = ⁴⁰₁₀₀ = ²₅

¹₅ Fabian = ²₅ Zane + 38 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x25x2 Fabian = 2x15x1 Zane + 38 
210 Fabian = 25 Zane + 38 

Simplify the fractions.
¹₁₀ Fabian = ¹₅ Zane + 19

Let ¹₅ Zane be 1 u.

Zane's savings at first = 5 u

¹₁₀ Fabian = ¹₅ Zane + 19
Let ¹₁₀ Fabian be 1 u + 19.

Fabian's savings at first
= 10 x (1 u + 19) 
= 10 u + 190

Savings that Zane spent
= 40% x 5 u
= ⁴⁰₁₀₀ x 5 u
= 2 u

Savings that Fabian spent 
= ¹₂ x (10 u + 190)
= 5 u + 95 

Fabian had $127 more than Zane in the end. If another $127 was given to Zane, the amount that each had in the end would be the same.

5 u + 95 = 3 u + 127 
5 u - 3 u = 127 - 95
2 u = 32

1 u = 32 ÷ 2 = 16

Savings that Fabian had at first
= 10 u + 190
= 10 x 16 + 190
= 160 + 190
= $350

Answer(s): $350