10% of Michael's savings was $24 more than 40% of Valen's savings. After Michael spent ⁷₁₀ of his savings and Valen spent 40% of his savings, Valen had $102 less than Michael. How much was Valen's saving at first?

	Valen	Michael
Before	5 u	20 u + 240
Change	- 2 u	- 14 u - 168
After	3 u	6 u + 72
Comparing Valen and Michael in the end		102 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Michael = ²₅ Valen + 24 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Michael = 2x15x1 Valen + 24 
220 Michael = 25 Valen + 24 

Simplify the fractions.
¹₂₀ Michael = ¹₅ Valen + 12

Let ¹₅ Valen be 1 u.

Valen's savings at first = 5 u

¹₂₀ Michael = ¹₅ Valen + 12
Let ¹₂₀ Michael be 1 u + 12.

Michael's savings at first
= 20 x (1 u + 12) 
= 20 u + 240

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

Savings that Michael spent 
= ⁷₁₀ x (20 u + 240)
= 14 u + 168 

Valen had $102 less than Michael in the end. If another $102 was given to Valen, the amount that each had in the end would be the same.

6 u + 72 = 3 u + 102 
6 u - 3 u = 102 - 72
3 u = 30

1 u = 30 ÷ 3 = 10

Savings that Valen had at first
= 5 u 
= 5 x 10
= $50

Answer(s): $50