20% of Reggie's savings was $6 more than 40% of Tom's savings. After Reggie spent ¹₅ of his savings and Tom spent 40% of his savings, Tom had $114 less than Reggie. How much was Tom's saving at first?

	Tom	Reggie
Before	5 u	10 u + 30
Change	- 2 u	- 2 u - 6
After	3 u	8 u + 24
Comparing Tom and Reggie in the end		114 more

20% = ²⁰₁₀₀ = ¹₅

40% = ⁴⁰₁₀₀ = ²₅

¹₅ Reggie = ²₅ Tom + 6 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x25x2 Reggie = 2x15x1 Tom + 6 
210 Reggie = 25 Tom + 6 

Simplify the fractions.
¹₁₀ Reggie = ¹₅ Tom + 3

Let ¹₅ Tom be 1 u.

Tom's savings at first = 5 u

¹₁₀ Reggie = ¹₅ Tom + 3
Let ¹₁₀ Reggie be 1 u + 3.

Reggie's savings at first
= 10 x (1 u + 3) 
= 10 u + 30

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

Savings that Reggie spent 
= ¹₅ x (10 u + 30)
= 2 u + 6 

Tom had $114 less than Reggie in the end. If another $114 was given to Tom, the amount that each had in the end would be the same.

8 u + 24 = 3 u + 114 
8 u - 3 u = 114 - 24
5 u = 90

1 u = 90 ÷ 5 = 18

Savings that Tom had at first
= 5 u 
= 5 x 18
= $90

Answer(s): $90