10% of Justin's savings was $18 more than 40% of Luis's savings. After Justin spent ¹₂ of his savings and Luis spent 40% of his savings, Luis had $153 less than Justin. How much was Luis's saving at first?

	Luis	Justin
Before	5 u	20 u + 180
Change	- 2 u	- 10 u - 90
After	3 u	10 u + 90
Comparing Luis and Justin in the end		153 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Justin = ²₅ Luis + 18 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Justin = 2x15x1 Luis + 18 
220 Justin = 25 Luis + 18 

Simplify the fractions.
¹₂₀ Justin = ¹₅ Luis + 9

Let ¹₅ Luis be 1 u.

Luis's savings at first = 5 u

¹₂₀ Justin = ¹₅ Luis + 9
Let ¹₂₀ Justin be 1 u + 9.

Justin's savings at first
= 20 x (1 u + 9) 
= 20 u + 180

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

Savings that Justin spent 
= ¹₂ x (20 u + 180)
= 10 u + 90 

Luis had $153 less than Justin in the end. If another $153 was given to Luis, the amount that each had in the end would be the same.

10 u + 90 = 3 u + 153 
10 u - 3 u = 153 - 90
7 u = 63

1 u = 63 ÷ 7 = 9

Savings that Luis had at first
= 5 u 
= 5 x 9
= $45

Answer(s): $45