25% of Peter's savings was $6 more than 30% of Neave's savings. After Peter spent ¹₄ of his savings and Neave spent 40% of his savings, Neave had $30 less than Peter. How much was Neave's saving at first?

	Neave	Peter
Before	10 u	12 u + 24
Change	- 4 u	- 3 u - 6
After	6 u	9 u + 18
Comparing Neave and Peter in the end		30 more

25% = ²⁵₁₀₀ = ¹₄

30% = ³⁰₁₀₀ = ³₁₀

¹₄ Peter = ³₁₀ Neave + 6 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x34x3 Peter = 3x110x1 Neave + 6 
312 Peter = 310 Neave + 6 

Simplify the fractions.
¹₁₂ Peter = ¹₁₀ Neave + 2

Let ¹₁₀ Neave be 1 u.

Neave's savings at first = 10 u

¹₁₂ Peter = ¹₁₀ Neave + 2
Let ¹₁₂ Peter be 1 u + 2.

Peter's savings at first
= 12 x (1 u + 2) 
= 12 u + 24

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

Savings that Peter spent 
= ¹₄ x (12 u + 24)
= 3 u + 6 

Neave had $30 less than Peter in the end. If another $30 was given to Neave, the amount that each had in the end would be the same.

9 u + 18 = 6 u + 30 
9 u - 6 u = 30 - 18
3 u = 12

1 u = 12 ÷ 3 = 4

Savings that Neave had at first
= 10 u 
= 10 x 4
= $40

Answer(s): $40