A number is divided into two parts in such a way that 80% of the first part is 3 more than 60% of the second part, and 80% of the second part is 6 more than 90% of the first part. The number is:
Answer: C
Let the parts be x and y.
1) 0.8x = 0.6y + 3 => 8x = 6y + 30 => 4x - 3y = 15
2) 0.8y = 0.9x + 6 => 8y = 9x + 60 => 9x - 8y = -60
Solving these two linear equations. Multiply (1) by 8 and (2) by 3:
32x - 24y = 120
27x - 24y = -180
Subtracting the second from the first gives: 5x = 300 => x = 60.
Substitute x=60 into (1): 4(60) - 3y = 15 => 240 - 3y = 15 => 225 = 3y => y = 75.
The number is the sum of the parts: x + y = 60 + 75 = 135.