10% of Rael's savings was $30 more than 30% of Neave's savings. After Rael spent ¹₅ of his savings and Neave spent 40% of his savings, Neave had $420 less than Rael. How much was Neave's saving at first?

	Neave	Rael
Before	10 u	30 u + 300
Change	- 4 u	- 6 u - 60
After	6 u	24 u + 240
Comparing Neave and Rael in the end		420 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Rael = ³₁₀ Neave + 30 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Rael = 3x110x1 Neave + 30 
330 Rael = 310 Neave + 30 

Simplify the fractions.
¹₃₀ Rael = ¹₁₀ Neave + 10

Let ¹₁₀ Neave be 1 u.

Neave's savings at first = 10 u

¹₃₀ Rael = ¹₁₀ Neave + 10
Let ¹₃₀ Rael be 1 u + 10.

Rael's savings at first
= 30 x (1 u + 10) 
= 30 u + 300

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

Savings that Rael spent 
= ¹₅ x (30 u + 300)
= 6 u + 60 

Neave had $420 less than Rael in the end. If another $420 was given to Neave, the amount that each had in the end would be the same.

24 u + 240 = 6 u + 420 
24 u - 6 u = 420 - 240
18 u = 180

1 u = 180 ÷ 18 = 10

Savings that Neave had at first
= 10 u 
= 10 x 10
= $100

Answer(s): $100