10% of Will's savings was $16 more than 40% of Julian's savings. After Will spent ³₄ of his savings and Julian spent 40% of his savings, Julian had $58 less than Will. How much was Julian's saving at first?

	Julian	Will
Before	5 u	20 u + 160
Change	- 2 u	- 15 u - 120
After	3 u	5 u + 40
Comparing Julian and Will in the end		58 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Will = ²₅ Julian + 16 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Will = 2x15x1 Julian + 16 
220 Will = 25 Julian + 16 

Simplify the fractions.
¹₂₀ Will = ¹₅ Julian + 8

Let ¹₅ Julian be 1 u.

Julian's savings at first = 5 u

¹₂₀ Will = ¹₅ Julian + 8
Let ¹₂₀ Will be 1 u + 8.

Will's savings at first
= 20 x (1 u + 8) 
= 20 u + 160

Savings that Julian spent
= 40% x 5 u
= ⁴⁰₁₀₀ x 5 u
= 2 u

Savings that Will spent 
= ³₄ x (20 u + 160)
= 15 u + 120 

Julian had $58 less than Will in the end. If another $58 was given to Julian, the amount that each had in the end would be the same.

5 u + 40 = 3 u + 58 
5 u - 3 u = 58 - 40
2 u = 18

1 u = 18 ÷ 2 = 9

Savings that Julian had at first
= 5 u 
= 5 x 9
= $45

Answer(s): $45