Robert needs to cut four shelves from a board that is 2.5 meters long. The second shelf is 18 cm longer than twice the length of the first shelf. The remaining shelf is 4 centimeters longer than the first shelf. If Robert must use the entire board for the shelves, what is the length of the second shelf, in cm
Accepted Solution
A:
STEP 1: convert meters to centimeters 100 cm= 1 meter
= 100 cm/m * 2.5 m = 250 cm
STEP 2: x= length of first shelf 2x+18= length of second shelf x-12= length of third shelf x+4= length of fourth shelf
since the whole board has to be used, add lengths of all shelves and set it equal to the whole length of the board (250 cm).
x + (2x+18) + (x-12) + (x+4)= 250 cm combine like terms 5x + 10= 250 subtract both sides by 10 5x= 240 divide both sides by 5 x= 48
STEP 3: find length of second shelf = 2x + 18 = 2(48) + 18 = 114 cm