20% of Andy's savings was $18 more than 30% of Carl's savings. After Andy spent ²₅ of his savings and Carl spent 40% of his savings, Carl had $105 less than Andy. How much was Carl's saving at first?

	Carl	Andy
Before	10 u	15 u + 90
Change	- 4 u	- 6 u - 36
After	6 u	9 u + 54
Comparing Carl and Andy in the end		105 more

20% = ²⁰₁₀₀ = ¹₅

30% = ³⁰₁₀₀ = ³₁₀

¹₅ Andy = ³₁₀ Carl + 18 

Make the numerators the same. LCM of 1 and 3 is 3.
 
1x35x3 Andy = 3x110x1 Carl + 18 
315 Andy = 310 Carl + 18 

Simplify the fractions.
¹₁₅ Andy = ¹₁₀ Carl + 6

Let ¹₁₀ Carl be 1 u.

Carl's savings at first = 10 u

¹₁₅ Andy = ¹₁₀ Carl + 6
Let ¹₁₅ Andy be 1 u + 6.

Andy's savings at first
= 15 x (1 u + 6) 
= 15 u + 90

Savings that Carl spent
= 40% x 10 u
= ⁴⁰₁₀₀ x 10 u
= 4 u

Savings that Andy spent 
= ²₅ x (15 u + 90)
= 6 u + 36 

Carl had $105 less than Andy in the end. If another $105 was given to Carl, the amount that each had in the end would be the same.

9 u + 54 = 6 u + 105 
9 u - 6 u = 105 - 54
3 u = 51

1 u = 51 ÷ 3 = 17

Savings that Carl had at first
= 10 u 
= 10 x 17
= $170

Answer(s): $170