20% of Liam's savings was $26 more than 40% of Jack's savings. After Liam spent ¹₂ of his savings and Jack spent 40% of his savings, Liam had $85 more than Jack. How much was Liam's saving at first?

	Jack	Liam
Before	5 u	10 u + 130
Change	- 2 u	- 5 u - 65
After	3 u	5 u + 65
Comparing Jack and Liam in the end		85 more

20% = ²⁰₁₀₀ = ¹₅

40% = ⁴⁰₁₀₀ = ²₅

¹₅ Liam = ²₅ Jack + 26 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x25x2 Liam = 2x15x1 Jack + 26 
210 Liam = 25 Jack + 26 

Simplify the fractions.
¹₁₀ Liam = ¹₅ Jack + 13

Let ¹₅ Jack be 1 u.

Jack's savings at first = 5 u

¹₁₀ Liam = ¹₅ Jack + 13
Let ¹₁₀ Liam be 1 u + 13.

Liam's savings at first
= 10 x (1 u + 13) 
= 10 u + 130

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

Savings that Liam spent 
= ¹₂ x (10 u + 130)
= 5 u + 65 

Liam had $85 more than Jack in the end. If another $85 was given to Jack, the amount that each had in the end would be the same.

5 u + 65 = 3 u + 85 
5 u - 3 u = 85 - 65
2 u = 20

1 u = 20 ÷ 2 = 10

Savings that Liam had at first
= 10 u + 130
= 10 x 10 + 130
= 100 + 130
= $230

Answer(s): $230