10% of Rael's savings was $60 more than 30% of Ivan's savings. After Rael spent ³₁₀ of his savings and Ivan spent 40% of his savings, Rael had $585 more than Ivan. How much was Rael's saving at first?

	Ivan	Rael
Before	10 u	30 u + 600
Change	- 4 u	- 9 u - 180
After	6 u	21 u + 420
Comparing Ivan and Rael in the end		585 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Rael = ³₁₀ Ivan + 60 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Rael = 3x110x1 Ivan + 60 
330 Rael = 310 Ivan + 60 

Simplify the fractions.
¹₃₀ Rael = ¹₁₀ Ivan + 20

Let ¹₁₀ Ivan be 1 u.

Ivan's savings at first = 10 u

¹₃₀ Rael = ¹₁₀ Ivan + 20
Let ¹₃₀ Rael be 1 u + 20.

Rael's savings at first
= 30 x (1 u + 20) 
= 30 u + 600

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

Savings that Rael spent 
= ³₁₀ x (30 u + 600)
= 9 u + 180 

Rael had $585 more than Ivan in the end. If another $585 was given to Ivan, the amount that each had in the end would be the same.

21 u + 420 = 6 u + 585 
21 u - 6 u = 585 - 420
15 u = 165

1 u = 165 ÷ 15 = 11

Savings that Rael had at first
= 30 u + 600
= 30 x 11 + 600
= 330 + 600
= $930

Answer(s): $930