10% of Elijah's savings was $27 more than 30% of Paul's savings. After Elijah spent ²₃ of his savings and Paul spent 40% of his savings, Paul had $158 less than Elijah. How much was Paul's saving at first?

	Paul	Elijah
Before	10 u	30 u + 270
Change	- 4 u	- 20 u - 180
After	6 u	10 u + 90
Comparing Paul and Elijah in the end		158 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Elijah = ³₁₀ Paul + 27 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Elijah = 3x110x1 Paul + 27 
330 Elijah = 310 Paul + 27 

Simplify the fractions.
¹₃₀ Elijah = ¹₁₀ Paul + 9

Let ¹₁₀ Paul be 1 u.

Paul's savings at first = 10 u

¹₃₀ Elijah = ¹₁₀ Paul + 9
Let ¹₃₀ Elijah be 1 u + 9.

Elijah's savings at first
= 30 x (1 u + 9) 
= 30 u + 270

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

Savings that Elijah spent 
= ²₃ x (30 u + 270)
= 20 u + 180 

Paul had $158 less than Elijah in the end. If another $158 was given to Paul, the amount that each had in the end would be the same.

10 u + 90 = 6 u + 158 
10 u - 6 u = 158 - 90
4 u = 68

1 u = 68 ÷ 4 = 17

Savings that Paul had at first
= 10 u 
= 10 x 17
= $170

Answer(s): $170