20% of Elijah's savings was $54 more than 30% of Will's savings. After Elijah spent ¹₃ of his savings and Will spent 40% of his savings, Elijah had $244 more than Will. How much was Elijah's saving at first?

	Will	Elijah
Before	10 u	15 u + 270
Change	- 4 u	- 5 u - 90
After	6 u	10 u + 180
Comparing Will and Elijah in the end		244 more

20% = ²⁰₁₀₀ = ¹₅

30% = ³⁰₁₀₀ = ³₁₀

¹₅ Elijah = ³₁₀ Will + 54 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x35x3 Elijah = 3x110x1 Will + 54 
315 Elijah = 310 Will + 54 

Simplify the fractions.
¹₁₅ Elijah = ¹₁₀ Will + 18

Let ¹₁₀ Will be 1 u.

Will's savings at first = 10 u

¹₁₅ Elijah = ¹₁₀ Will + 18
Let ¹₁₅ Elijah be 1 u + 18.

Elijah's savings at first
= 15 x (1 u + 18) 
= 15 u + 270

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

Savings that Elijah spent 
= ¹₃ x (15 u + 270)
= 5 u + 90 

Elijah had $244 more than Will in the end. If another $244 was given to Will, the amount that each had in the end would be the same.

10 u + 180 = 6 u + 244 
10 u - 6 u = 244 - 180
4 u = 64

1 u = 64 ÷ 4 = 16

Savings that Elijah had at first
= 15 u + 270
= 15 x 16 + 270
= 240 + 270
= $510

Answer(s): $510