20% of Asher's savings was $51 more than 30% of Simon's savings. After Asher spent ¹₅ of his savings and Simon spent 40% of his savings, Simon had $324 less than Asher. How much was Simon's saving at first?

	Simon	Asher
Before	10 u	15 u + 255
Change	- 4 u	- 3 u - 51
After	6 u	12 u + 204
Comparing Simon and Asher in the end		324 more

20% = ²⁰₁₀₀ = ¹₅

30% = ³⁰₁₀₀ = ³₁₀

¹₅ Asher = ³₁₀ Simon + 51 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x35x3 Asher = 3x110x1 Simon + 51 
315 Asher = 310 Simon + 51 

Simplify the fractions.
¹₁₅ Asher = ¹₁₀ Simon + 17

Let ¹₁₀ Simon be 1 u.

Simon's savings at first = 10 u

¹₁₅ Asher = ¹₁₀ Simon + 17
Let ¹₁₅ Asher be 1 u + 17.

Asher's savings at first
= 15 x (1 u + 17) 
= 15 u + 255

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

Savings that Asher spent 
= ¹₅ x (15 u + 255)
= 3 u + 51 

Simon had $324 less than Asher in the end. If another $324 was given to Simon, the amount that each had in the end would be the same.

12 u + 204 = 6 u + 324 
12 u - 6 u = 324 - 204
6 u = 120

1 u = 120 ÷ 6 = 20

Savings that Simon had at first
= 10 u 
= 10 x 20
= $200

Answer(s): $200