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Question 1107624: 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?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a = the first shelf.
b = the second shelf.
c = the third shelf.
d = the fourth shelf.
b = 2a + 18
c = a - 12
d = a + 4
2.5 meters = 250 centimeters.
a + b + c + d = 250 centimeters.
replace b with 2a + 18 and replace c with a - 12 and replace d with a + 4 and you get:
a + 2a + 18 + a - 12 + a + 4 = 250
combine like terms to get 5a + 10 = 250
subtract 10 from both sides of the equation to get 5a = 240
solve for a to get a = 48.
you get:
a = 48
b = 2a + 18 = 114
c = a - 12 = 36
d = a + 4 = 52
the total of all the boards is equal to 48 + 114 + 36 + 52 = 250 centimeters.
the measurements check out ok.
your solution is that the second shelf, which is b, is equal to 114 centimeters.
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