25% of Bryan's savings was $8 more than 40% of Zeph's savings. After Bryan spent ¹₄ of his savings and Zeph spent 40% of his savings, Zeph had $78 less than Bryan. How much was Zeph's saving at first?

	Zeph	Bryan
Before	5 u	8 u + 32
Change	- 2 u	- 2 u - 8
After	3 u	6 u + 24
Comparing Zeph and Bryan in the end		78 more

25% = ²⁵₁₀₀ = ¹₄

40% = ⁴⁰₁₀₀ = ²₅

¹₄ Bryan = ²₅ Zeph + 8 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x24x2 Bryan = 2x15x1 Zeph + 8 
28 Bryan = 25 Zeph + 8 

Simplify the fractions.
¹₈ Bryan = ¹₅ Zeph + 4

Let ¹₅ Zeph be 1 u.

Zeph's savings at first = 5 u

¹₈ Bryan = ¹₅ Zeph + 4
Let ¹₈ Bryan be 1 u + 4.

Bryan's savings at first
= 8 x (1 u + 4) 
= 8 u + 32

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

Savings that Bryan spent 
= ¹₄ x (8 u + 32)
= 2 u + 8 

Zeph had $78 less than Bryan in the end. If another $78 was given to Zeph, the amount that each had in the end would be the same.

6 u + 24 = 3 u + 78 
6 u - 3 u = 78 - 24
3 u = 54

1 u = 54 ÷ 3 = 18

Savings that Zeph had at first
= 5 u 
= 5 x 18
= $90

Answer(s): $90