10% of Carl's savings was $15 more than 30% of Zeph's savings. After Carl spent ²₅ of his savings and Zeph spent 40% of his savings, Zeph had $138 less than Carl. How much was Zeph's saving at first?

	Zeph	Carl
Before	10 u	30 u + 150
Change	- 4 u	- 12 u - 60
After	6 u	18 u + 90
Comparing Zeph and Carl in the end		138 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Carl = ³₁₀ Zeph + 15 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Carl = 3x110x1 Zeph + 15 
330 Carl = 310 Zeph + 15 

Simplify the fractions.
¹₃₀ Carl = ¹₁₀ Zeph + 5

Let ¹₁₀ Zeph be 1 u.

Zeph's savings at first = 10 u

¹₃₀ Carl = ¹₁₀ Zeph + 5
Let ¹₃₀ Carl be 1 u + 5.

Carl's savings at first
= 30 x (1 u + 5) 
= 30 u + 150

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

Savings that Carl spent 
= ²₅ x (30 u + 150)
= 12 u + 60 

Zeph had $138 less than Carl in the end. If another $138 was given to Zeph, the amount that each had in the end would be the same.

18 u + 90 = 6 u + 138 
18 u - 6 u = 138 - 90
12 u = 48

1 u = 48 ÷ 12 = 4

Savings that Zeph had at first
= 10 u 
= 10 x 4
= $40

Answer(s): $40