10% of Caden's savings was $30 more than 30% of Jeremy's savings. After Caden spent ²₃ of his savings and Jeremy spent 40% of his savings, Caden had $160 more than Jeremy. How much was Caden's saving at first?

	Jeremy	Caden
Before	10 u	30 u + 300
Change	- 4 u	- 20 u - 200
After	6 u	10 u + 100
Comparing Jeremy and Caden in the end		160 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Caden = ³₁₀ Jeremy + 30 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Caden = 3x110x1 Jeremy + 30 
330 Caden = 310 Jeremy + 30 

Simplify the fractions.
¹₃₀ Caden = ¹₁₀ Jeremy + 10

Let ¹₁₀ Jeremy be 1 u.

Jeremy's savings at first = 10 u

¹₃₀ Caden = ¹₁₀ Jeremy + 10
Let ¹₃₀ Caden be 1 u + 10.

Caden's savings at first
= 30 x (1 u + 10) 
= 30 u + 300

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

Savings that Caden spent 
= ²₃ x (30 u + 300)
= 20 u + 200 

Caden had $160 more than Jeremy in the end. If another $160 was given to Jeremy, the amount that each had in the end would be the same.

10 u + 100 = 6 u + 160 
10 u - 6 u = 160 - 100
4 u = 60

1 u = 60 ÷ 4 = 15

Savings that Caden had at first
= 30 u + 300
= 30 x 15 + 300
= 450 + 300
= $750

Answer(s): $750