25% of Vincent's savings was $18 more than 30% of Bobby's savings. After Vincent spent ¹₃ of his savings and Bobby spent 40% of his savings, Bobby had $76 less than Vincent. How much was Bobby's saving at first?

	Bobby	Vincent
Before	10 u	12 u + 72
Change	- 4 u	- 4 u - 24
After	6 u	8 u + 48
Comparing Bobby and Vincent in the end		76 more

25% = ²⁵₁₀₀ = ¹₄

30% = ³⁰₁₀₀ = ³₁₀

¹₄ Vincent = ³₁₀ Bobby + 18 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x34x3 Vincent = 3x110x1 Bobby + 18 
312 Vincent = 310 Bobby + 18 

Simplify the fractions.
¹₁₂ Vincent = ¹₁₀ Bobby + 6

Let ¹₁₀ Bobby be 1 u.

Bobby's savings at first = 10 u

¹₁₂ Vincent = ¹₁₀ Bobby + 6
Let ¹₁₂ Vincent be 1 u + 6.

Vincent's savings at first
= 12 x (1 u + 6) 
= 12 u + 72

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

Savings that Vincent spent 
= ¹₃ x (12 u + 72)
= 4 u + 24 

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

8 u + 48 = 6 u + 76 
8 u - 6 u = 76 - 48
2 u = 28

1 u = 28 ÷ 2 = 14

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

Answer(s): $140