The length of the second shelf is 114 centimetres.
Consider the four shelves as A, B, C and D. According to the question, the length of the four shelves is 2.5 cm.
A + B + C + D = 250 cm ( 1 m = 100 cm ⇒ 2.5 * 100 = 250 ) → 1
The length of the second shelf is 18 cm longer than twice the length of the first shelf.
B = 2A + 18 → i
The length of the third shelf is 12 cm shorter than the first shelf.
C = A - 12 → ii
The length of the fourth shelf is 4 cm longer than the first shelf.
D = A + 4 → iii
Substitute i,ii and iii in 1 ⇒ A + B + C + D = 250
A + 2A + 18 + A - 12 + A + 4 = 250
5A + 22 - 12 = 250
5A + 10 = 250
5A = 250 - 10
5A = 240
A = 240/5
A = 48
Substitute A = 48 in i, ii, iii and then we get,
B = 11, C = 36 and D = 52
Therefore, the length of the second shelf B is 114 cm.
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The complete question is
Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 centimetres longer than twice the length of the first shelf. The third shelf is 12 centimetres shorter than the first shelf. The remaining shelf is 4 centimetres 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 centimetres?
