10% of Henry's savings was $8 more than 40% of Reggie's savings. After Henry spent ³₄ of his savings and Reggie spent 40% of his savings, Henry had $48 more than Reggie. How much was Henry's saving at first?

	Reggie	Henry
Before	5 u	20 u + 80
Change	- 2 u	- 15 u - 60
After	3 u	5 u + 20
Comparing Reggie and Henry in the end		48 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Henry = ²₅ Reggie + 8 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Henry = 2x15x1 Reggie + 8 
220 Henry = 25 Reggie + 8 

Simplify the fractions.
¹₂₀ Henry = ¹₅ Reggie + 4

Let ¹₅ Reggie be 1 u.

Reggie's savings at first = 5 u

¹₂₀ Henry = ¹₅ Reggie + 4
Let ¹₂₀ Henry be 1 u + 4.

Henry's savings at first
= 20 x (1 u + 4) 
= 20 u + 80

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

Savings that Henry spent 
= ³₄ x (20 u + 80)
= 15 u + 60 

Henry had $48 more than Reggie in the end. If another $48 was given to Reggie, the amount that each had in the end would be the same.

5 u + 20 = 3 u + 48 
5 u - 3 u = 48 - 20
2 u = 28

1 u = 28 ÷ 2 = 14

Savings that Henry had at first
= 20 u + 80
= 20 x 14 + 80
= 280 + 80
= $360

Answer(s): $360