10% of Cole's savings was $33 more than 30% of Sean's savings. After Cole spent ¹₃ of his savings and Sean spent 40% of his savings, Cole had $346 more than Sean. How much was Cole's saving at first?

	Sean	Cole
Before	10 u	30 u + 330
Change	- 4 u	- 10 u - 110
After	6 u	20 u + 220
Comparing Sean and Cole in the end		346 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Cole = ³₁₀ Sean + 33 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Cole = 3x110x1 Sean + 33 
330 Cole = 310 Sean + 33 

Simplify the fractions.
¹₃₀ Cole = ¹₁₀ Sean + 11

Let ¹₁₀ Sean be 1 u.

Sean's savings at first = 10 u

¹₃₀ Cole = ¹₁₀ Sean + 11
Let ¹₃₀ Cole be 1 u + 11.

Cole's savings at first
= 30 x (1 u + 11) 
= 30 u + 330

Savings that Sean spent
= 40% x 10 u
= ⁴⁰₁₀₀ x 10 u
= 4 u

Savings that Cole spent 
= ¹₃ x (30 u + 330)
= 10 u + 110 

Cole had $346 more than Sean in the end. If another $346 was given to Sean, the amount that each had in the end would be the same.

20 u + 220 = 6 u + 346 
20 u - 6 u = 346 - 220
14 u = 126

1 u = 126 ÷ 14 = 9

Savings that Cole had at first
= 30 u + 330
= 30 x 9 + 330
= 270 + 330
= $600

Answer(s): $600