20% of Luke's savings was $36 more than 30% of Flynn's savings. After Luke spent ¹₅ of his savings and Flynn spent 40% of his savings, Flynn had $234 less than Luke. How much was Flynn's saving at first?

	Flynn	Luke
Before	10 u	15 u + 180
Change	- 4 u	- 3 u - 36
After	6 u	12 u + 144
Comparing Flynn and Luke in the end		234 more

20% = ²⁰₁₀₀ = ¹₅

30% = ³⁰₁₀₀ = ³₁₀

¹₅ Luke = ³₁₀ Flynn + 36 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x35x3 Luke = 3x110x1 Flynn + 36 
315 Luke = 310 Flynn + 36 

Simplify the fractions.
¹₁₅ Luke = ¹₁₀ Flynn + 12

Let ¹₁₀ Flynn be 1 u.

Flynn's savings at first = 10 u

¹₁₅ Luke = ¹₁₀ Flynn + 12
Let ¹₁₅ Luke be 1 u + 12.

Luke's savings at first
= 15 x (1 u + 12) 
= 15 u + 180

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

Savings that Luke spent 
= ¹₅ x (15 u + 180)
= 3 u + 36 

Flynn had $234 less than Luke in the end. If another $234 was given to Flynn, the amount that each had in the end would be the same.

12 u + 144 = 6 u + 234 
12 u - 6 u = 234 - 144
6 u = 90

1 u = 90 ÷ 6 = 15

Savings that Flynn had at first
= 10 u 
= 10 x 15
= $150

Answer(s): $150