MATH SOLVE

8 months ago

Q:
# robert needs to cut 4 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?

Accepted Solution

A:

The second shelf is 114 cm.

Let x be the length of the first shelf.Β Then the second shelf is 2x+18; the third shelf is x-12; and the fourth shelf is x+4.Β The total length is 2.5 meters; since there are 100 cm in 1 meter, there are 2.5*100 = 250 cm in this board.

All of the four shelves add up to 250

x + (2x+18) + (x-12) + (x+4) = 250

Combining like terms we have

5x + 10 = 250

Subtract 10 from both sides:

5x + 10 - 10 = 250 - 10

5x = 240

Divide both sides by 5:

5x/5 = 240/5

x = 48

The second shelf was 2x+18:

2(48)+18 = 114 cm

Let x be the length of the first shelf.Β Then the second shelf is 2x+18; the third shelf is x-12; and the fourth shelf is x+4.Β The total length is 2.5 meters; since there are 100 cm in 1 meter, there are 2.5*100 = 250 cm in this board.

All of the four shelves add up to 250

x + (2x+18) + (x-12) + (x+4) = 250

Combining like terms we have

5x + 10 = 250

Subtract 10 from both sides:

5x + 10 - 10 = 250 - 10

5x = 240

Divide both sides by 5:

5x/5 = 240/5

x = 48

The second shelf was 2x+18:

2(48)+18 = 114 cm