Robert needs to cut for shelves from a board that is 2.5 m long. the second shelf is 18 cm longer than twice the length of the first shelf. the third shelf is 12 cm shorter than the first shelf. the remaining shelf is 4 cm longer than the first shelf. if Robert must use the entire 2.5 m board for the shelves what is the length of the second shelf in centimeters
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To find the length of the second shelf, let's first assign variables to the lengths of the shelves. Let's say the length of the first shelf is x cm.
Given that the second shelf is 18 cm longer than twice the length of the first shelf, we can express it as: 2x + 18 cm.
The third shelf is 12 cm shorter than the first shelf, so its length would be: x - 12 cm.
And finally, the remaining shelf is 4 cm longer than the first shelf, which means its length is: x + 4 cm.
Now, we need to sum up the lengths of all the shelves and set it equal to the length of the board, which is 2.5 m or 250 cm.
x + 2x + 18 + x - 12 + x + 4 = 250
Combine like terms:
5x + 10 = 250
Subtract 10 from both sides:
5x = 240
Divide both sides by 5:
x = 48
So, the length of the first shelf is 48 cm.
To find the length of the second shelf, which is 18 cm longer than twice the length of the first shelf, we substitute x = 48 into the expression: 2x + 18.
2(48) + 18 = 96 + 18 = 114 cm
Therefore, the length of the second shelf is 114 cm.