10% of Dylan's savings was $27 more than 30% of Julian's savings. After Dylan spent ²₃ of his savings and Julian spent 40% of his savings, Dylan had $122 more than Julian. How much was Dylan's saving at first?

	Julian	Dylan
Before	10 u	30 u + 270
Change	- 4 u	- 20 u - 180
After	6 u	10 u + 90
Comparing Julian and Dylan in the end		122 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Dylan = ³₁₀ Julian + 27 

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

Simplify the fractions.
¹₃₀ Dylan = ¹₁₀ Julian + 9

Let ¹₁₀ Julian be 1 u.

Julian's savings at first = 10 u

¹₃₀ Dylan = ¹₁₀ Julian + 9
Let ¹₃₀ Dylan be 1 u + 9.

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

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

Savings that Dylan spent 
= ²₃ x (30 u + 270)
= 20 u + 180 

Dylan had $122 more than Julian in the end. If another $122 was given to Julian, the amount that each had in the end would be the same.

10 u + 90 = 6 u + 122 
10 u - 6 u = 122 - 90
4 u = 32

1 u = 32 ÷ 4 = 8

Savings that Dylan had at first
= 30 u + 270
= 30 x 8 + 270
= 240 + 270
= $510

Answer(s): $510