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?

Question

Ryann

Mathematics

25 September, 20:01

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?

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Answers (1)

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Hailee Kerr · Answer 1

114cm / 1.14m

If we call the length of the first shelf x, shelf two is 2x+18, shelf 3 is x-12 and shelf 4 is x+4.

The total length of board is 250cm

the total length of the shelves is 5x+10 and the whole board is used so 5x+10 = 250

5x = 240 (-10 from both sides)

x = 48 (divide both sides by 5)

board 2 is 2x+18

2 x = 96+18

= 114cm