20% of Mark's savings was $10 more than 40% of Sam's savings. After Mark spent ²₅ of his savings and Sam spent 40% of his savings, Mark had $39 more than Sam. How much was Mark's saving at first?

	Sam	Mark
Before	5 u	10 u + 50
Change	- 2 u	- 4 u - 20
After	3 u	6 u + 30
Comparing Sam and Mark in the end		39 more

20% = ²⁰₁₀₀ = ¹₅

40% = ⁴⁰₁₀₀ = ²₅

¹₅ Mark = ²₅ Sam + 10 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x25x2 Mark = 2x15x1 Sam + 10 
210 Mark = 25 Sam + 10 

Simplify the fractions.
¹₁₀ Mark = ¹₅ Sam + 5

Let ¹₅ Sam be 1 u.

Sam's savings at first = 5 u

¹₁₀ Mark = ¹₅ Sam + 5
Let ¹₁₀ Mark be 1 u + 5.

Mark's savings at first
= 10 x (1 u + 5) 
= 10 u + 50

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

Savings that Mark spent 
= ²₅ x (10 u + 50)
= 4 u + 20 

Mark had $39 more than Sam in the end. If another $39 was given to Sam, the amount that each had in the end would be the same.

6 u + 30 = 3 u + 39 
6 u - 3 u = 39 - 30
3 u = 9

1 u = 9 ÷ 3 = 3

Savings that Mark had at first
= 10 u + 50
= 10 x 3 + 50
= 30 + 50
= $80

Answer(s): $80