10% of Tommy's savings was $27 more than 30% of Jack's savings. After Tommy spent ¹₃ of his savings and Jack spent 40% of his savings, Jack had $208 less than Tommy. How much was Jack's saving at first?

	Jack	Tommy
Before	10 u	30 u + 270
Change	- 4 u	- 10 u - 90
After	6 u	20 u + 180
Comparing Jack and Tommy in the end		208 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Tommy = ³₁₀ Jack + 27 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Tommy = 3x110x1 Jack + 27 
330 Tommy = 310 Jack + 27 

Simplify the fractions.
¹₃₀ Tommy = ¹₁₀ Jack + 9

Let ¹₁₀ Jack be 1 u.

Jack's savings at first = 10 u

¹₃₀ Tommy = ¹₁₀ Jack + 9
Let ¹₃₀ Tommy be 1 u + 9.

Tommy's savings at first
= 30 x (1 u + 9) 
= 30 u + 270

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

Savings that Tommy spent 
= ¹₃ x (30 u + 270)
= 10 u + 90 

Jack had $208 less than Tommy in the end. If another $208 was given to Jack, the amount that each had in the end would be the same.

20 u + 180 = 6 u + 208 
20 u - 6 u = 208 - 180
14 u = 28

1 u = 28 ÷ 14 = 2

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

Answer(s): $20