25% of Japheth's savings was $45 more than 30% of Neave's savings. After Japheth spent ¹₆ of his savings and Neave spent 40% of his savings, Neave had $226 less than Japheth. How much was Neave's saving at first?

	Neave	Japheth
Before	10 u	12 u + 180
Change	- 4 u	- 2 u - 30
After	6 u	10 u + 150
Comparing Neave and Japheth in the end		226 more

25% = ²⁵₁₀₀ = ¹₄

30% = ³⁰₁₀₀ = ³₁₀

¹₄ Japheth = ³₁₀ Neave + 45 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x34x3 Japheth = 3x110x1 Neave + 45 
312 Japheth = 310 Neave + 45 

Simplify the fractions.
¹₁₂ Japheth = ¹₁₀ Neave + 15

Let ¹₁₀ Neave be 1 u.

Neave's savings at first = 10 u

¹₁₂ Japheth = ¹₁₀ Neave + 15
Let ¹₁₂ Japheth be 1 u + 15.

Japheth's savings at first
= 12 x (1 u + 15) 
= 12 u + 180

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

Savings that Japheth spent 
= ¹₆ x (12 u + 180)
= 2 u + 30 

Neave had $226 less than Japheth in the end. If another $226 was given to Neave, the amount that each had in the end would be the same.

10 u + 150 = 6 u + 226 
10 u - 6 u = 226 - 150
4 u = 76

1 u = 76 ÷ 4 = 19

Savings that Neave had at first
= 10 u 
= 10 x 19
= $190

Answer(s): $190