25% of David's savings was $27 more than 30% of Reggie's savings. After David spent ¹₄ of his savings and Reggie spent 40% of his savings, David had $111 more than Reggie. How much was David's saving at first?

	Reggie	David
Before	10 u	12 u + 108
Change	- 4 u	- 3 u - 27
After	6 u	9 u + 81
Comparing Reggie and David in the end		111 more

25% = ²⁵₁₀₀ = ¹₄

30% = ³⁰₁₀₀ = ³₁₀

¹₄ David = ³₁₀ Reggie + 27 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x34x3 David = 3x110x1 Reggie + 27 
312 David = 310 Reggie + 27 

Simplify the fractions.
¹₁₂ David = ¹₁₀ Reggie + 9

Let ¹₁₀ Reggie be 1 u.

Reggie's savings at first = 10 u

¹₁₂ David = ¹₁₀ Reggie + 9
Let ¹₁₂ David be 1 u + 9.

David's savings at first
= 12 x (1 u + 9) 
= 12 u + 108

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

Savings that David spent 
= ¹₄ x (12 u + 108)
= 3 u + 27 

David had $111 more than Reggie in the end. If another $111 was given to Reggie, the amount that each had in the end would be the same.

9 u + 81 = 6 u + 111 
9 u - 6 u = 111 - 81
3 u = 30

1 u = 30 ÷ 3 = 10

Savings that David had at first
= 12 u + 108
= 12 x 10 + 108
= 120 + 108
= $228

Answer(s): $228