10% of Charlie's savings was $36 more than 40% of Harry's savings. After Charlie spent ¹₅ of his savings and Harry spent 40% of his savings, Charlie had $353 more than Harry. How much was Charlie's saving at first?

	Harry	Charlie
Before	5 u	20 u + 360
Change	- 2 u	- 4 u - 72
After	3 u	16 u + 288
Comparing Harry and Charlie in the end		353 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Charlie = ²₅ Harry + 36 

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

Simplify the fractions.
¹₂₀ Charlie = ¹₅ Harry + 18

Let ¹₅ Harry be 1 u.

Harry's savings at first = 5 u

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

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

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

Savings that Charlie spent 
= ¹₅ x (20 u + 360)
= 4 u + 72 

Charlie had $353 more than Harry in the end. If another $353 was given to Harry, the amount that each had in the end would be the same.

16 u + 288 = 3 u + 353 
16 u - 3 u = 353 - 288
13 u = 65

1 u = 65 ÷ 13 = 5

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

Answer(s): $460