20% of Ben's savings was $4 more than 40% of Luke's savings. After Ben spent ¹₂ of his savings and Luke spent 40% of his savings, Ben had $20 more than Luke. How much was Ben's saving at first?

	Luke	Ben
Before	5 u	10 u + 20
Change	- 2 u	- 5 u - 10
After	3 u	5 u + 10
Comparing Luke and Ben in the end		20 more

20% = ²⁰₁₀₀ = ¹₅

40% = ⁴⁰₁₀₀ = ²₅

¹₅ Ben = ²₅ Luke + 4 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x25x2 Ben = 2x15x1 Luke + 4 
210 Ben = 25 Luke + 4 

Simplify the fractions.
¹₁₀ Ben = ¹₅ Luke + 2

Let ¹₅ Luke be 1 u.

Luke's savings at first = 5 u

¹₁₀ Ben = ¹₅ Luke + 2
Let ¹₁₀ Ben be 1 u + 2.

Ben's savings at first
= 10 x (1 u + 2) 
= 10 u + 20

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

Savings that Ben spent 
= ¹₂ x (10 u + 20)
= 5 u + 10 

Ben had $20 more than Luke in the end. If another $20 was given to Luke, the amount that each had in the end would be the same.

5 u + 10 = 3 u + 20 
5 u - 3 u = 20 - 10
2 u = 10

1 u = 10 ÷ 2 = 5

Savings that Ben had at first
= 10 u + 20
= 10 x 5 + 20
= 50 + 20
= $70

Answer(s): $70