20% of Jack's savings was $24 more than 30% of Ethan's savings. After Jack spent ¹₅ of his savings and Ethan spent 40% of his savings, Ethan had $210 less than Jack. How much was Ethan's saving at first?

	Ethan	Jack
Before	10 u	15 u + 120
Change	- 4 u	- 3 u - 24
After	6 u	12 u + 96
Comparing Ethan and Jack in the end		210 more

20% = ²⁰₁₀₀ = ¹₅

30% = ³⁰₁₀₀ = ³₁₀

¹₅ Jack = ³₁₀ Ethan + 24 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x35x3 Jack = 3x110x1 Ethan + 24 
315 Jack = 310 Ethan + 24 

Simplify the fractions.
¹₁₅ Jack = ¹₁₀ Ethan + 8

Let ¹₁₀ Ethan be 1 u.

Ethan's savings at first = 10 u

¹₁₅ Jack = ¹₁₀ Ethan + 8
Let ¹₁₅ Jack be 1 u + 8.

Jack's savings at first
= 15 x (1 u + 8) 
= 15 u + 120

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

Savings that Jack spent 
= ¹₅ x (15 u + 120)
= 3 u + 24 

Ethan had $210 less than Jack in the end. If another $210 was given to Ethan, the amount that each had in the end would be the same.

12 u + 96 = 6 u + 210 
12 u - 6 u = 210 - 96
6 u = 114

1 u = 114 ÷ 6 = 19

Savings that Ethan had at first
= 10 u 
= 10 x 19
= $190

Answer(s): $190