20% of Bryan's savings was $14 more than 40% of Julian's savings. After Bryan spent ²₅ of his savings and Julian spent 40% of his savings, Julian had $75 less than Bryan. How much was Julian's saving at first?

	Julian	Bryan
Before	5 u	10 u + 70
Change	- 2 u	- 4 u - 28
After	3 u	6 u + 42
Comparing Julian and Bryan in the end		75 more

20% = ²⁰₁₀₀ = ¹₅

40% = ⁴⁰₁₀₀ = ²₅

¹₅ Bryan = ²₅ Julian + 14 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x25x2 Bryan = 2x15x1 Julian + 14 
210 Bryan = 25 Julian + 14 

Simplify the fractions.
¹₁₀ Bryan = ¹₅ Julian + 7

Let ¹₅ Julian be 1 u.

Julian's savings at first = 5 u

¹₁₀ Bryan = ¹₅ Julian + 7
Let ¹₁₀ Bryan be 1 u + 7.

Bryan's savings at first
= 10 x (1 u + 7) 
= 10 u + 70

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

Savings that Bryan spent 
= ²₅ x (10 u + 70)
= 4 u + 28 

Julian had $75 less than Bryan in the end. If another $75 was given to Julian, the amount that each had in the end would be the same.

6 u + 42 = 3 u + 75 
6 u - 3 u = 75 - 42
3 u = 33

1 u = 33 ÷ 3 = 11

Savings that Julian had at first
= 5 u 
= 5 x 11
= $55

Answer(s): $55