10% of Michael's savings was $22 more than 40% of Mark's savings. After Michael spent ¹₂ of his savings and Mark spent 40% of his savings, Michael had $215 more than Mark. How much was Michael's saving at first?

	Mark	Michael
Before	5 u	20 u + 220
Change	- 2 u	- 10 u - 110
After	3 u	10 u + 110
Comparing Mark and Michael in the end		215 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Michael = ²₅ Mark + 22 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Michael = 2x15x1 Mark + 22 
220 Michael = 25 Mark + 22 

Simplify the fractions.
¹₂₀ Michael = ¹₅ Mark + 11

Let ¹₅ Mark be 1 u.

Mark's savings at first = 5 u

¹₂₀ Michael = ¹₅ Mark + 11
Let ¹₂₀ Michael be 1 u + 11.

Michael's savings at first
= 20 x (1 u + 11) 
= 20 u + 220

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

Savings that Michael spent 
= ¹₂ x (20 u + 220)
= 10 u + 110 

Michael had $215 more than Mark in the end. If another $215 was given to Mark, the amount that each had in the end would be the same.

10 u + 110 = 3 u + 215 
10 u - 3 u = 215 - 110
7 u = 105

1 u = 105 ÷ 7 = 15

Savings that Michael had at first
= 20 u + 220
= 20 x 15 + 220
= 300 + 220
= $520

Answer(s): $520