10% of Charlie's savings was $36 more than 40% of Sam's savings. After Charlie spent ³₄ of his savings and Sam spent 40% of his savings, Charlie had $100 more than Sam. How much was Charlie's saving at first?

	Sam	Charlie
Before	5 u	20 u + 360
Change	- 2 u	- 15 u - 270
After	3 u	5 u + 90
Comparing Sam and Charlie in the end		100 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Charlie = ²₅ Sam + 36 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Charlie = 2x15x1 Sam + 36 
220 Charlie = 25 Sam + 36 

Simplify the fractions.
¹₂₀ Charlie = ¹₅ Sam + 18

Let ¹₅ Sam be 1 u.

Sam's savings at first = 5 u

¹₂₀ Charlie = ¹₅ Sam + 18
Let ¹₂₀ Charlie be 1 u + 18.

Charlie's savings at first
= 20 x (1 u + 18) 
= 20 u + 360

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

Savings that Charlie spent 
= ³₄ x (20 u + 360)
= 15 u + 270 

Charlie had $100 more than Sam in the end. If another $100 was given to Sam, the amount that each had in the end would be the same.

5 u + 90 = 3 u + 100 
5 u - 3 u = 100 - 90
2 u = 10

1 u = 10 ÷ 2 = 5

Savings that Charlie had at first
= 20 u + 360
= 20 x 5 + 360
= 100 + 360
= $460

Answer(s): $460