20% of Charlie's savings was $33 more than 30% of Justin's savings. After Charlie spent ²₅ of his savings and Justin spent 40% of his savings, Charlie had $135 more than Justin. How much was Charlie's saving at first?

	Justin	Charlie
Before	10 u	15 u + 165
Change	- 4 u	- 6 u - 66
After	6 u	9 u + 99
Comparing Justin and Charlie in the end		135 more

20% = ²⁰₁₀₀ = ¹₅

30% = ³⁰₁₀₀ = ³₁₀

¹₅ Charlie = ³₁₀ Justin + 33 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x35x3 Charlie = 3x110x1 Justin + 33 
315 Charlie = 310 Justin + 33 

Simplify the fractions.
¹₁₅ Charlie = ¹₁₀ Justin + 11

Let ¹₁₀ Justin be 1 u.

Justin's savings at first = 10 u

¹₁₅ Charlie = ¹₁₀ Justin + 11
Let ¹₁₅ Charlie be 1 u + 11.

Charlie's savings at first
= 15 x (1 u + 11) 
= 15 u + 165

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

Savings that Charlie spent 
= ²₅ x (15 u + 165)
= 6 u + 66 

Charlie had $135 more than Justin in the end. If another $135 was given to Justin, the amount that each had in the end would be the same.

9 u + 99 = 6 u + 135 
9 u - 6 u = 135 - 99
3 u = 36

1 u = 36 ÷ 3 = 12

Savings that Charlie had at first
= 15 u + 165
= 15 x 12 + 165
= 180 + 165
= $345

Answer(s): $345