10% of Elijah's savings was $6 more than 30% of Nick's savings. After Elijah spent ²₃ of his savings and Nick spent 40% of his savings, Nick had $76 less than Elijah. How much was Nick's saving at first?

	Nick	Elijah
Before	10 u	30 u + 60
Change	- 4 u	- 20 u - 40
After	6 u	10 u + 20
Comparing Nick and Elijah in the end		76 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Elijah = ³₁₀ Nick + 6 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Elijah = 3x110x1 Nick + 6 
330 Elijah = 310 Nick + 6 

Simplify the fractions.
¹₃₀ Elijah = ¹₁₀ Nick + 2

Let ¹₁₀ Nick be 1 u.

Nick's savings at first = 10 u

¹₃₀ Elijah = ¹₁₀ Nick + 2
Let ¹₃₀ Elijah be 1 u + 2.

Elijah's savings at first
= 30 x (1 u + 2) 
= 30 u + 60

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

Savings that Elijah spent 
= ²₃ x (30 u + 60)
= 20 u + 40 

Nick had $76 less than Elijah in the end. If another $76 was given to Nick, the amount that each had in the end would be the same.

10 u + 20 = 6 u + 76 
10 u - 6 u = 76 - 20
4 u = 56

1 u = 56 ÷ 4 = 14

Savings that Nick had at first
= 10 u 
= 10 x 14
= $140

Answer(s): $140