20% of Bryan's savings was $57 more than 30% of Ben's savings. After Bryan spent ¹₃ of his savings and Ben spent 40% of his savings, Ben had $226 less than Bryan. How much was Ben's saving at first?

	Ben	Bryan
Before	10 u	15 u + 285
Change	- 4 u	- 5 u - 95
After	6 u	10 u + 190
Comparing Ben and Bryan in the end		226 more

20% = ²⁰₁₀₀ = ¹₅

30% = ³⁰₁₀₀ = ³₁₀

¹₅ Bryan = ³₁₀ Ben + 57 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x35x3 Bryan = 3x110x1 Ben + 57 
315 Bryan = 310 Ben + 57 

Simplify the fractions.
¹₁₅ Bryan = ¹₁₀ Ben + 19

Let ¹₁₀ Ben be 1 u.

Ben's savings at first = 10 u

¹₁₅ Bryan = ¹₁₀ Ben + 19
Let ¹₁₅ Bryan be 1 u + 19.

Bryan's savings at first
= 15 x (1 u + 19) 
= 15 u + 285

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

Savings that Bryan spent 
= ¹₃ x (15 u + 285)
= 5 u + 95 

Ben had $226 less than Bryan in the end. If another $226 was given to Ben, the amount that each had in the end would be the same.

10 u + 190 = 6 u + 226 
10 u - 6 u = 226 - 190
4 u = 36

1 u = 36 ÷ 4 = 9

Savings that Ben had at first
= 10 u 
= 10 x 9
= $90

Answer(s): $90