10% of Brandon's savings was $32 more than 40% of Michael's savings. After Brandon spent ¹₄ of his savings and Michael spent 40% of his savings, Brandon had $288 more than Michael. How much was Brandon's saving at first?

	Michael	Brandon
Before	5 u	20 u + 320
Change	- 2 u	- 5 u - 80
After	3 u	15 u + 240
Comparing Michael and Brandon in the end		288 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Brandon = ²₅ Michael + 32 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Brandon = 2x15x1 Michael + 32 
220 Brandon = 25 Michael + 32 

Simplify the fractions.
¹₂₀ Brandon = ¹₅ Michael + 16

Let ¹₅ Michael be 1 u.

Michael's savings at first = 5 u

¹₂₀ Brandon = ¹₅ Michael + 16
Let ¹₂₀ Brandon be 1 u + 16.

Brandon's savings at first
= 20 x (1 u + 16) 
= 20 u + 320

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

Savings that Brandon spent 
= ¹₄ x (20 u + 320)
= 5 u + 80 

Brandon had $288 more than Michael in the end. If another $288 was given to Michael, the amount that each had in the end would be the same.

15 u + 240 = 3 u + 288 
15 u - 3 u = 288 - 240
12 u = 48

1 u = 48 ÷ 12 = 4

Savings that Brandon had at first
= 20 u + 320
= 20 x 4 + 320
= 80 + 320
= $400

Answer(s): $400