25% of Julian's savings was $36 more than 30% of Paul's savings. After Julian spent ¹₃ of his savings and Paul spent 40% of his savings, Julian had $130 more than Paul. How much was Julian's saving at first?

	Paul	Julian
Before	10 u	12 u + 144
Change	- 4 u	- 4 u - 48
After	6 u	8 u + 96
Comparing Paul and Julian in the end		130 more

25% = ²⁵₁₀₀ = ¹₄

30% = ³⁰₁₀₀ = ³₁₀

¹₄ Julian = ³₁₀ Paul + 36 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x34x3 Julian = 3x110x1 Paul + 36 
312 Julian = 310 Paul + 36 

Simplify the fractions.
¹₁₂ Julian = ¹₁₀ Paul + 12

Let ¹₁₀ Paul be 1 u.

Paul's savings at first = 10 u

¹₁₂ Julian = ¹₁₀ Paul + 12
Let ¹₁₂ Julian be 1 u + 12.

Julian's savings at first
= 12 x (1 u + 12) 
= 12 u + 144

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

Savings that Julian spent 
= ¹₃ x (12 u + 144)
= 4 u + 48 

Julian had $130 more than Paul in the end. If another $130 was given to Paul, the amount that each had in the end would be the same.

8 u + 96 = 6 u + 130 
8 u - 6 u = 130 - 96
2 u = 34

1 u = 34 ÷ 2 = 17

Savings that Julian had at first
= 12 u + 144
= 12 x 17 + 144
= 204 + 144
= $348

Answer(s): $348