10% of Tommy's savings was $30 more than 40% of Perry's savings. After Tommy spent ¹₅ of his savings and Perry spent 40% of his savings, Perry had $357 less than Tommy. How much was Perry's saving at first?

	Perry	Tommy
Before	5 u	20 u + 300
Change	- 2 u	- 4 u - 60
After	3 u	16 u + 240
Comparing Perry and Tommy in the end		357 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Tommy = ²₅ Perry + 30 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Tommy = 2x15x1 Perry + 30 
220 Tommy = 25 Perry + 30 

Simplify the fractions.
¹₂₀ Tommy = ¹₅ Perry + 15

Let ¹₅ Perry be 1 u.

Perry's savings at first = 5 u

¹₂₀ Tommy = ¹₅ Perry + 15
Let ¹₂₀ Tommy be 1 u + 15.

Tommy's savings at first
= 20 x (1 u + 15) 
= 20 u + 300

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

Savings that Tommy spent 
= ¹₅ x (20 u + 300)
= 4 u + 60 

Perry had $357 less than Tommy in the end. If another $357 was given to Perry, the amount that each had in the end would be the same.

16 u + 240 = 3 u + 357 
16 u - 3 u = 357 - 240
13 u = 117

1 u = 117 ÷ 13 = 9

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

Answer(s): $45