Problem:
A number is divided into two parts such that 80% of the first part is 3 more than 60% of the second part, and 6 more than 90% of the first part is equal to the second part. Find the number.

Solution:
Let's assume the number to be divided into two parts is "x".

Step 1: Convert the given statements into equations.
- 80% of the first part is 3 more than 60% of the second part: 0.8(first part) = 0.6(second part) + 3
- 6 more than 90% of the first part is equal to the second part: 0.9(first part) + 6 = second part

Step 2: Simplify the equations.
- 0.8(first part) = 0.6(second part) + 3 can be simplified as 0.8(first part) - 0.6(second part) = 3
- 0.9(first part) + 6 = second part can be simplified as 0.9(first part) - second part = -6

Step 3: Solve the equations simultaneously.
We can solve these equations by substitution or elimination method. Let's use the elimination method to solve them.

Multiplying the first equation by 10, we get:
8(first part) - 6(second part) = 30 --(Equation 1)
0.9(first part) - second part = -6 --(Equation 2)

To eliminate the second part, let's multiply Equation 2 by 6:
5.4(first part) - 6(second part) = -36 --(Equation 3)

Subtracting Equation 3 from Equation 1:
(8(first part) - 5.4(first part)) - (-6(second part) + 6(second part)) = 30 - (-36)
2.6(first part) = 66
first part = 66/2.6
first part = 25.38

Substituting the value of first part in Equation 2:
0.9(25.38) - second part = -6
22.842 - second part = -6
second part = 22.842 + 6
second part = 28.842

Step 4: Calculate the number.
Since the number is divided into two parts, the number can be calculated as the sum of the two parts.
Number = first part + second part
Number = 25.38 + 28.842
Number = 54.222

Therefore, the number is 54.222.