20% of Bobby's savings was $18 more than 30% of Zeph's savings. After Bobby spent ²₅ of his savings and Zeph spent 40% of his savings, Bobby had $105 more than Zeph. How much was Bobby's saving at first?

	Zeph	Bobby
Before	10 u	15 u + 90
Change	- 4 u	- 6 u - 36
After	6 u	9 u + 54
Comparing Zeph and Bobby in the end		105 more

20% = ²⁰₁₀₀ = ¹₅

30% = ³⁰₁₀₀ = ³₁₀

¹₅ Bobby = ³₁₀ Zeph + 18 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x35x3 Bobby = 3x110x1 Zeph + 18 
315 Bobby = 310 Zeph + 18 

Simplify the fractions.
¹₁₅ Bobby = ¹₁₀ Zeph + 6

Let ¹₁₀ Zeph be 1 u.

Zeph's savings at first = 10 u

¹₁₅ Bobby = ¹₁₀ Zeph + 6
Let ¹₁₅ Bobby be 1 u + 6.

Bobby's savings at first
= 15 x (1 u + 6) 
= 15 u + 90

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

Savings that Bobby spent 
= ²₅ x (15 u + 90)
= 6 u + 36 

Bobby had $105 more than Zeph in the end. If another $105 was given to Zeph, the amount that each had in the end would be the same.

9 u + 54 = 6 u + 105 
9 u - 6 u = 105 - 54
3 u = 51

1 u = 51 ÷ 3 = 17

Savings that Bobby had at first
= 15 u + 90
= 15 x 17 + 90
= 255 + 90
= $345

Answer(s): $345