10% of Rael's savings was $27 more than 30% of Howard's savings. After Rael spent ²₅ of his savings and Howard spent 40% of his savings, Rael had $330 more than Howard. How much was Rael's saving at first?

	Howard	Rael
Before	10 u	30 u + 270
Change	- 4 u	- 12 u - 108
After	6 u	18 u + 162
Comparing Howard and Rael in the end		330 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Rael = ³₁₀ Howard + 27 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Rael = 3x110x1 Howard + 27 
330 Rael = 310 Howard + 27 

Simplify the fractions.
¹₃₀ Rael = ¹₁₀ Howard + 9

Let ¹₁₀ Howard be 1 u.

Howard's savings at first = 10 u

¹₃₀ Rael = ¹₁₀ Howard + 9
Let ¹₃₀ Rael be 1 u + 9.

Rael's savings at first
= 30 x (1 u + 9) 
= 30 u + 270

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

Savings that Rael spent 
= ²₅ x (30 u + 270)
= 12 u + 108 

Rael had $330 more than Howard in the end. If another $330 was given to Howard, the amount that each had in the end would be the same.

18 u + 162 = 6 u + 330 
18 u - 6 u = 330 - 162
12 u = 168

1 u = 168 ÷ 12 = 14

Savings that Rael had at first
= 30 u + 270
= 30 x 14 + 270
= 420 + 270
= $690

Answer(s): $690