20% of John's savings was $4 more than 40% of Caden's savings. After John spent ²₅ of his savings and Caden spent 40% of his savings, John had $51 more than Caden. How much was John's saving at first?

	Caden	John
Before	5 u	10 u + 20
Change	- 2 u	- 4 u - 8
After	3 u	6 u + 12
Comparing Caden and John in the end		51 more

20% = ²⁰₁₀₀ = ¹₅

40% = ⁴⁰₁₀₀ = ²₅

¹₅ John = ²₅ Caden + 4 

Make the numerators the same. LCM of 1 and 2 is 2.
 
1x25x2 John = 2x15x1 Caden + 4 
210 John = 25 Caden + 4 

Simplify the fractions.
¹₁₀ John = ¹₅ Caden + 2

Let ¹₅ Caden be 1 u.

Caden's savings at first = 5 u

¹₁₀ John = ¹₅ Caden + 2
Let ¹₁₀ John be 1 u + 2.

John's savings at first
= 10 x (1 u + 2) 
= 10 u + 20

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

Savings that John spent 
= ²₅ x (10 u + 20)
= 4 u + 8 

John had $51 more than Caden in the end. If another $51 was given to Caden, the amount that each had in the end would be the same.

6 u + 12 = 3 u + 51 
6 u - 3 u = 51 - 12
3 u = 39

1 u = 39 ÷ 3 = 13

Savings that John had at first
= 10 u + 20
= 10 x 13 + 20
= 130 + 20
= $150

Answer(s): $150