10% of Bryan's savings was $30 more than 40% of Neave's savings. After Bryan spent ⁷₁₀ of his savings and Neave spent 40% of his savings, Neave had $138 less than Bryan. How much was Neave's saving at first?

	Neave	Bryan
Before	5 u	20 u + 300
Change	- 2 u	- 14 u - 210
After	3 u	6 u + 90
Comparing Neave and Bryan in the end		138 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Bryan = ²₅ Neave + 30 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Bryan = 2x15x1 Neave + 30 
220 Bryan = 25 Neave + 30 

Simplify the fractions.
¹₂₀ Bryan = ¹₅ Neave + 15

Let ¹₅ Neave be 1 u.

Neave's savings at first = 5 u

¹₂₀ Bryan = ¹₅ Neave + 15
Let ¹₂₀ Bryan be 1 u + 15.

Bryan's savings at first
= 20 x (1 u + 15) 
= 20 u + 300

Savings that Neave spent
= 40% x 5 u
= ⁴⁰₁₀₀ x 5 u
= 2 u

Savings that Bryan spent 
= ⁷₁₀ x (20 u + 300)
= 14 u + 210 

Neave had $138 less than Bryan in the end. If another $138 was given to Neave, the amount that each had in the end would be the same.

6 u + 90 = 3 u + 138 
6 u - 3 u = 138 - 90
3 u = 48

1 u = 48 ÷ 3 = 16

Savings that Neave had at first
= 5 u 
= 5 x 16
= $80

Answer(s): $80