10% of Neave's savings was $40 more than 40% of Daniel's savings. After Neave spent ³₄ of his savings and Daniel spent 40% of his savings, Neave had $124 more than Daniel. How much was Neave's saving at first?

	Daniel	Neave
Before	5 u	20 u + 400
Change	- 2 u	- 15 u - 300
After	3 u	5 u + 100
Comparing Daniel and Neave in the end		124 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Neave = ²₅ Daniel + 40 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Neave = 2x15x1 Daniel + 40 
220 Neave = 25 Daniel + 40 

Simplify the fractions.
¹₂₀ Neave = ¹₅ Daniel + 20

Let ¹₅ Daniel be 1 u.

Daniel's savings at first = 5 u

¹₂₀ Neave = ¹₅ Daniel + 20
Let ¹₂₀ Neave be 1 u + 20.

Neave's savings at first
= 20 x (1 u + 20) 
= 20 u + 400

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

Savings that Neave spent 
= ³₄ x (20 u + 400)
= 15 u + 300 

Neave had $124 more than Daniel in the end. If another $124 was given to Daniel, the amount that each had in the end would be the same.

5 u + 100 = 3 u + 124 
5 u - 3 u = 124 - 100
2 u = 24

1 u = 24 ÷ 2 = 12

Savings that Neave had at first
= 20 u + 400
= 20 x 12 + 400
= 240 + 400
= $640

Answer(s): $640