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, in centimeters?

there are 100 centimeters in a meter. 

therefore 2.5 meters = 2.5 * 100 = 250 centimeters. 

x = the length of the first board.
2x + 18 = the length of the second board.
x - 12 = the length of the third board.
x + 4 = the length of the fourth board. 

the total length of all the boards is equal to 5x + 10, 

since the total length of the board is 250 centimeters, then you get: 

5x + 10 = 250 

solve for x to get x = 48 centimeters. 

the 4 board lengths are: 

x = 48
2x + 18 = 114
x - 12 = 36
x + 4 = 52 

add them up and you get a total of 250 centimeters. 

250 centimeters / 100 = 2.5 meters. 

this confirms the solution is good.