10% of Carl's savings was $18 more than 30% of Gabriel's savings. After Carl spent ²₅ of his savings and Gabriel spent 40% of his savings, Carl had $240 more than Gabriel. How much was Carl's saving at first?

	Gabriel	Carl
Before	10 u	30 u + 180
Change	- 4 u	- 12 u - 72
After	6 u	18 u + 108
Comparing Gabriel and Carl in the end		240 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Carl = ³₁₀ Gabriel + 18 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Carl = 3x110x1 Gabriel + 18 
330 Carl = 310 Gabriel + 18 

Simplify the fractions.
¹₃₀ Carl = ¹₁₀ Gabriel + 6

Let ¹₁₀ Gabriel be 1 u.

Gabriel's savings at first = 10 u

¹₃₀ Carl = ¹₁₀ Gabriel + 6
Let ¹₃₀ Carl be 1 u + 6.

Carl's savings at first
= 30 x (1 u + 6) 
= 30 u + 180

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

Savings that Carl spent 
= ²₅ x (30 u + 180)
= 12 u + 72 

Carl had $240 more than Gabriel in the end. If another $240 was given to Gabriel, the amount that each had in the end would be the same.

18 u + 108 = 6 u + 240 
18 u - 6 u = 240 - 108
12 u = 132

1 u = 132 ÷ 12 = 11

Savings that Carl had at first
= 30 u + 180
= 30 x 11 + 180
= 330 + 180
= $510

Answer(s): $510