10% of Tommy's savings was $28 more than 40% of Nick's savings. After Tommy spent ¹₂ of his savings and Nick spent 40% of his savings, Nick had $175 less than Tommy. How much was Nick's saving at first?

	Nick	Tommy
Before	5 u	20 u + 280
Change	- 2 u	- 10 u - 140
After	3 u	10 u + 140
Comparing Nick and Tommy in the end		175 more

10% = ¹⁰₁₀₀ = ¹₁₀

40% = ⁴⁰₁₀₀ = ²₅

¹₁₀ Tommy = ²₅ Nick + 28 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x210x2 Tommy = 2x15x1 Nick + 28 
220 Tommy = 25 Nick + 28 

Simplify the fractions.
¹₂₀ Tommy = ¹₅ Nick + 14

Let ¹₅ Nick be 1 u.

Nick's savings at first = 5 u

¹₂₀ Tommy = ¹₅ Nick + 14
Let ¹₂₀ Tommy be 1 u + 14.

Tommy's savings at first
= 20 x (1 u + 14) 
= 20 u + 280

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

Savings that Tommy spent 
= ¹₂ x (20 u + 280)
= 10 u + 140 

Nick had $175 less than Tommy in the end. If another $175 was given to Nick, the amount that each had in the end would be the same.

10 u + 140 = 3 u + 175 
10 u - 3 u = 175 - 140
7 u = 35

1 u = 35 ÷ 7 = 5

Savings that Nick had at first
= 5 u 
= 5 x 5
= $25

Answer(s): $25