20% of Ethan's savings was $36 more than 40% of Bryan's savings. After Ethan spent ¹₅ of his savings and Bryan spent 40% of his savings, Bryan had $224 less than Ethan. How much was Bryan's saving at first?

	Bryan	Ethan
Before	5 u	10 u + 180
Change	- 2 u	- 2 u - 36
After	3 u	8 u + 144
Comparing Bryan and Ethan in the end		224 more

20% = ²⁰₁₀₀ = ¹₅

40% = ⁴⁰₁₀₀ = ²₅

¹₅ Ethan = ²₅ Bryan + 36 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x25x2 Ethan = 2x15x1 Bryan + 36 
210 Ethan = 25 Bryan + 36 

Simplify the fractions.
¹₁₀ Ethan = ¹₅ Bryan + 18

Let ¹₅ Bryan be 1 u.

Bryan's savings at first = 5 u

¹₁₀ Ethan = ¹₅ Bryan + 18
Let ¹₁₀ Ethan be 1 u + 18.

Ethan's savings at first
= 10 x (1 u + 18) 
= 10 u + 180

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

Savings that Ethan spent 
= ¹₅ x (10 u + 180)
= 2 u + 36 

Bryan had $224 less than Ethan in the end. If another $224 was given to Bryan, the amount that each had in the end would be the same.

8 u + 144 = 3 u + 224 
8 u - 3 u = 224 - 144
5 u = 80

1 u = 80 ÷ 5 = 16

Savings that Bryan had at first
= 5 u 
= 5 x 16
= $80

Answer(s): $80