10% of Charlie's savings was $36 more than 30% of Simon's savings. After Charlie spent ¹₂ of his savings and Simon spent 40% of his savings, Simon had $198 less than Charlie. How much was Simon's saving at first?

	Simon	Charlie
Before	10 u	30 u + 360
Change	- 4 u	- 15 u - 180
After	6 u	15 u + 180
Comparing Simon and Charlie in the end		198 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Charlie = ³₁₀ Simon + 36 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Charlie = 3x110x1 Simon + 36 
330 Charlie = 310 Simon + 36 

Simplify the fractions.
¹₃₀ Charlie = ¹₁₀ Simon + 12

Let ¹₁₀ Simon be 1 u.

Simon's savings at first = 10 u

¹₃₀ Charlie = ¹₁₀ Simon + 12
Let ¹₃₀ Charlie be 1 u + 12.

Charlie's savings at first
= 30 x (1 u + 12) 
= 30 u + 360

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

Savings that Charlie spent 
= ¹₂ x (30 u + 360)
= 15 u + 180 

Simon had $198 less than Charlie in the end. If another $198 was given to Simon, the amount that each had in the end would be the same.

15 u + 180 = 6 u + 198 
15 u - 6 u = 198 - 180
9 u = 18

1 u = 18 ÷ 9 = 2

Savings that Simon had at first
= 10 u 
= 10 x 2
= $20

Answer(s): $20