10% of Archie's savings was $24 more than 30% of Oliver's savings. After Archie spent ²₃ of his savings and Oliver spent 40% of his savings, Oliver had $152 less than Archie. How much was Oliver's saving at first?

	Oliver	Archie
Before	10 u	30 u + 240
Change	- 4 u	- 20 u - 160
After	6 u	10 u + 80
Comparing Oliver and Archie in the end		152 more

10% = ¹⁰₁₀₀ = ¹₁₀

30% = ³⁰₁₀₀ = ³₁₀

¹₁₀ Archie = ³₁₀ Oliver + 24 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x310x3 Archie = 3x110x1 Oliver + 24 
330 Archie = 310 Oliver + 24 

Simplify the fractions.
¹₃₀ Archie = ¹₁₀ Oliver + 8

Let ¹₁₀ Oliver be 1 u.

Oliver's savings at first = 10 u

¹₃₀ Archie = ¹₁₀ Oliver + 8
Let ¹₃₀ Archie be 1 u + 8.

Archie's savings at first
= 30 x (1 u + 8) 
= 30 u + 240

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

Savings that Archie spent 
= ²₃ x (30 u + 240)
= 20 u + 160 

Oliver had $152 less than Archie in the end. If another $152 was given to Oliver, the amount that each had in the end would be the same.

10 u + 80 = 6 u + 152 
10 u - 6 u = 152 - 80
4 u = 72

1 u = 72 ÷ 4 = 18

Savings that Oliver had at first
= 10 u 
= 10 x 18
= $180

Answer(s): $180