10% of Tim's savings was $15 more than 30% of David's savings. After Tim spent ¹₃ of his savings and David spent 40% of his savings, David had $282 less than Tim. How much was David's saving at first?

	David	Tim
Before	10 u	30 u + 150
Change	- 4 u	- 10 u - 50
After	6 u	20 u + 100
Comparing David and Tim in the end		282 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Tim = ³₁₀ David + 15 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Tim = 3x110x1 David + 15 
330 Tim = 310 David + 15 

Simplify the fractions.
¹₃₀ Tim = ¹₁₀ David + 5

Let ¹₁₀ David be 1 u.

David's savings at first = 10 u

¹₃₀ Tim = ¹₁₀ David + 5
Let ¹₃₀ Tim be 1 u + 5.

Tim's savings at first
= 30 x (1 u + 5) 
= 30 u + 150

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

Savings that Tim spent 
= ¹₃ x (30 u + 150)
= 10 u + 50 

David had $282 less than Tim in the end. If another $282 was given to David, the amount that each had in the end would be the same.

20 u + 100 = 6 u + 282 
20 u - 6 u = 282 - 100
14 u = 182

1 u = 182 ÷ 14 = 13

Savings that David had at first
= 10 u 
= 10 x 13
= $130

Answer(s): $130