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?
first shelf ---- x cm
2nd shelf --- 2x+18 cm
3rd shelf ---- x-12 cm
4th shelf ---- x+4
clearly: x + 2x+18 + x-12 + x+4 = 250
solve for x
(are you not worried about the width of each saw-cut that is lost ?)
To find the length of the second shelf, let's assign variables to the lengths of the shelves.
Let's call the length of the first shelf "x" (in centimeters).
According to the problem, the second shelf is 18 centimeters longer than twice the length of the first shelf, so its length would be 2x + 18.
The third shelf is 12 centimeters shorter than the first shelf, so its length would be x - 12.
The remaining shelf is 4 centimeters longer than the first shelf, so its length would be x + 4.
Since Robert needs to cut all four shelves from a board that is 2.5 meters long, we need to convert this length to centimeters. There are 100 centimeters in a meter, so the board is 2.5 * 100 = 250 centimeters long.
To determine the total length of the four shelves, we add all the shelf lengths together: x + (2x + 18) + (x - 12) + (x + 4) = 250.
Simplifying the equation gives us 5x + 10 = 250.
Subtracting 10 from both sides gives us 5x = 240.
Dividing both sides by 5 gives us x = 48.
Therefore, the length of the second shelf is calculated as 2x + 18 = 2(48) + 18 = 96 + 18 = 114 centimeters.