20% of Rael's savings was $28 more than 40% of Elijah's savings. After Rael spent ¹₅ of his savings and Elijah spent 40% of his savings, Elijah had $127 less than Rael. How much was Elijah's saving at first?

	Elijah	Rael
Before	5 u	10 u + 140
Change	- 2 u	- 2 u - 28
After	3 u	8 u + 112
Comparing Elijah and Rael in the end		127 more

20% = ²⁰₁₀₀ = ¹₅

40% = ⁴⁰₁₀₀ = ²₅

¹₅ Rael = ²₅ Elijah + 28 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x25x2 Rael = 2x15x1 Elijah + 28 
210 Rael = 25 Elijah + 28 

Simplify the fractions.
¹₁₀ Rael = ¹₅ Elijah + 14

Let ¹₅ Elijah be 1 u.

Elijah's savings at first = 5 u

¹₁₀ Rael = ¹₅ Elijah + 14
Let ¹₁₀ Rael be 1 u + 14.

Rael's savings at first
= 10 x (1 u + 14) 
= 10 u + 140

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

Savings that Rael spent 
= ¹₅ x (10 u + 140)
= 2 u + 28 

Elijah had $127 less than Rael in the end. If another $127 was given to Elijah, the amount that each had in the end would be the same.

8 u + 112 = 3 u + 127 
8 u - 3 u = 127 - 112
5 u = 15

1 u = 15 ÷ 5 = 3

Savings that Elijah had at first
= 5 u 
= 5 x 3
= $15

Answer(s): $15