20% of Howard's savings was $39 more than 30% of Japheth's savings. After Howard spent ¹₃ of his savings and Japheth spent 40% of his savings, Howard had $146 more than Japheth. How much was Howard's saving at first?

	Japheth	Howard
Before	10 u	15 u + 195
Change	- 4 u	- 5 u - 65
After	6 u	10 u + 130
Comparing Japheth and Howard in the end		146 more

20% = ²⁰₁₀₀ = ¹₅

30% = ³⁰₁₀₀ = ³₁₀

¹₅ Howard = ³₁₀ Japheth + 39 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x35x3 Howard = 3x110x1 Japheth + 39 
315 Howard = 310 Japheth + 39 

Simplify the fractions.
¹₁₅ Howard = ¹₁₀ Japheth + 13

Let ¹₁₀ Japheth be 1 u.

Japheth's savings at first = 10 u

¹₁₅ Howard = ¹₁₀ Japheth + 13
Let ¹₁₅ Howard be 1 u + 13.

Howard's savings at first
= 15 x (1 u + 13) 
= 15 u + 195

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

Savings that Howard spent 
= ¹₃ x (15 u + 195)
= 5 u + 65 

Howard had $146 more than Japheth in the end. If another $146 was given to Japheth, the amount that each had in the end would be the same.

10 u + 130 = 6 u + 146 
10 u - 6 u = 146 - 130
4 u = 16

1 u = 16 ÷ 4 = 4

Savings that Howard had at first
= 15 u + 195
= 15 x 4 + 195
= 60 + 195
= $255

Answer(s): $255