10% of Zane's savings was $12 more than 40% of Cody's savings. After Zane spent ¹₂ of his savings and Cody spent 40% of his savings, Cody had $165 less than Zane. How much was Cody's saving at first?

	Cody	Zane
Before	5 u	20 u + 120
Change	- 2 u	- 10 u - 60
After	3 u	10 u + 60
Comparing Cody and Zane in the end		165 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Zane = ²₅ Cody + 12 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Zane = 2x15x1 Cody + 12 
220 Zane = 25 Cody + 12 

Simplify the fractions.
¹₂₀ Zane = ¹₅ Cody + 6

Let ¹₅ Cody be 1 u.

Cody's savings at first = 5 u

¹₂₀ Zane = ¹₅ Cody + 6
Let ¹₂₀ Zane be 1 u + 6.

Zane's savings at first
= 20 x (1 u + 6) 
= 20 u + 120

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

Savings that Zane spent 
= ¹₂ x (20 u + 120)
= 10 u + 60 

Cody had $165 less than Zane in the end. If another $165 was given to Cody, the amount that each had in the end would be the same.

10 u + 60 = 3 u + 165 
10 u - 3 u = 165 - 60
7 u = 105

1 u = 105 ÷ 7 = 15

Savings that Cody had at first
= 5 u 
= 5 x 15
= $75

Answer(s): $75