Roger had some rope with a total length 24 m. He used 2/3 of the rope to tie a wooden structure for outdoor cooking and 3/4 of the remaining rope to strengthen the pegs for his tent. How much rope did he have left? Give your answer in meters.
L = length of rope
If he used 2 / 3 of the rope then remaining rope = L - 2 / 3 L =
3 / 3 L - 2 / 3 L = 1 / 3 L
If he used 3 / 4 of the remaining rope to strengthen the pegs for his tent, he used:
3 / 4 ∙ 1 / 3 L = 1 / 4 L
Totally he used:
2 / 3 L + 1 / 4 L = 2 ∙ 4 / 3 ∙ 4 L + 3 ∙ 1 / 3 ∙ 4 L =
8 / 12 L + 3 / 12 L = 11 / 12 L
He left:
L - 11 / 12 L = 12 / 12 L - 11 / 12 L = 1 / 12 L = 24 m / 12 = 2 m rope