10% of Owen's savings was $40 more than 40% of Oscar's savings. After Owen spent ¹₄ of his savings and Oscar spent 40% of his savings, Owen had $516 more than Oscar. How much was Owen's saving at first?

	Oscar	Owen
Before	5 u	20 u + 400
Change	- 2 u	- 5 u - 100
After	3 u	15 u + 300
Comparing Oscar and Owen in the end		516 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Owen = ²₅ Oscar + 40 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Owen = 2x15x1 Oscar + 40 
220 Owen = 25 Oscar + 40 

Simplify the fractions.
¹₂₀ Owen = ¹₅ Oscar + 20

Let ¹₅ Oscar be 1 u.

Oscar's savings at first = 5 u

¹₂₀ Owen = ¹₅ Oscar + 20
Let ¹₂₀ Owen be 1 u + 20.

Owen's savings at first
= 20 x (1 u + 20) 
= 20 u + 400

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

Savings that Owen spent 
= ¹₄ x (20 u + 400)
= 5 u + 100 

Owen had $516 more than Oscar in the end. If another $516 was given to Oscar, the amount that each had in the end would be the same.

15 u + 300 = 3 u + 516 
15 u - 3 u = 516 - 300
12 u = 216

1 u = 216 ÷ 12 = 18

Savings that Owen had at first
= 20 u + 400
= 20 x 18 + 400
= 360 + 400
= $760

Answer(s): $760