Robert needs to cut four shelves from a board that is 2.5 meters long. the second shelf is 18 centimeters longer than twice the length of the first shelf. the third shelf is 12 centimeters shorter than the first shelf. the remaining shelf is 4 centimeters longer than the first shelf. if robert must use the entire 2.5 meter board for the shelves, what is the length of the second shelf?

Let us assume the length of the first shelf = x
Then
The length of the second shelf = 2x + 18
Length of the third shelf = x -12
Length of the fourth shelf = x + 4
The total length of the board = 2.5 meters.
                                              = ( 2.5 * 100) cm
                                               = 250 cm
Then we can write the equation as
x + 2x + 18 + x - 12 + x + 4 = 250
5x + 10 = 250
After dividing both sides of the equation by 5 we get
x + 2 = 50
x = 50 - 2
   = 48
Then
The length of the second shelf = 2x + 18
                                                 = 2(48) + 18
                                                 = 96 + 18
                                                 = 116
So the length of the second shelf is 116 cm.