10% of Ryan's savings was $40 more than 40% of Riordan's savings. After Ryan spent ¹₅ of his savings and Riordan spent 40% of his savings, Riordan had $554 less than Ryan. How much was Riordan's saving at first?

	Riordan	Ryan
Before	5 u	20 u + 400
Change	- 2 u	- 4 u - 80
After	3 u	16 u + 320
Comparing Riordan and Ryan in the end		554 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Ryan = ²₅ Riordan + 40 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Ryan = 2x15x1 Riordan + 40 
220 Ryan = 25 Riordan + 40 

Simplify the fractions.
¹₂₀ Ryan = ¹₅ Riordan + 20

Let ¹₅ Riordan be 1 u.

Riordan's savings at first = 5 u

¹₂₀ Ryan = ¹₅ Riordan + 20
Let ¹₂₀ Ryan be 1 u + 20.

Ryan's savings at first
= 20 x (1 u + 20) 
= 20 u + 400

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

Savings that Ryan spent 
= ¹₅ x (20 u + 400)
= 4 u + 80 

Riordan had $554 less than Ryan in the end. If another $554 was given to Riordan, the amount that each had in the end would be the same.

16 u + 320 = 3 u + 554 
16 u - 3 u = 554 - 320
13 u = 234

1 u = 234 ÷ 13 = 18

Savings that Riordan had at first
= 5 u 
= 5 x 18
= $90

Answer(s): $90