10% of Cole's savings was $30 more than 40% of Xavier's savings. After Cole spent ¹₂ of his savings and Xavier spent 40% of his savings, Xavier had $290 less than Cole. How much was Xavier's saving at first?

	Xavier	Cole
Before	5 u	20 u + 300
Change	- 2 u	- 10 u - 150
After	3 u	10 u + 150
Comparing Xavier and Cole in the end		290 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Cole = ²₅ Xavier + 30 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Cole = 2x15x1 Xavier + 30 
220 Cole = 25 Xavier + 30 

Simplify the fractions.
¹₂₀ Cole = ¹₅ Xavier + 15

Let ¹₅ Xavier be 1 u.

Xavier's savings at first = 5 u

¹₂₀ Cole = ¹₅ Xavier + 15
Let ¹₂₀ Cole be 1 u + 15.

Cole's savings at first
= 20 x (1 u + 15) 
= 20 u + 300

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

Savings that Cole spent 
= ¹₂ x (20 u + 300)
= 10 u + 150 

Xavier had $290 less than Cole in the end. If another $290 was given to Xavier, the amount that each had in the end would be the same.

10 u + 150 = 3 u + 290 
10 u - 3 u = 290 - 150
7 u = 140

1 u = 140 ÷ 7 = 20

Savings that Xavier had at first
= 5 u 
= 5 x 20
= $100

Answer(s): $100