Answer: D = 134
Step-by-step explanation:
The parameters given are
Mean = 68cm
Median = 84cm
Assuming the length of the ropes starting from the shortest to the longest are a, b , c , 84, e, f, g
since the length of the shortest rope = a, the length of the longest rope from the question will be = 14 + 4a
. therefore g now becomes 14 + 4a
Mean = (total sum of the rope length / number of ropes)
Therefore the total sum of the rope length = mean x number of ropes
= 84 x 7 = 476.
since we are to find the maximum possible length of the longest piece of rope, it is safe to assume that the ropes b and c are of the same length as the first rope since they would still be less than the length of the median rope which is 84cm in length. It is also safe to assume that ropes e and f are of the same length as the median rope since they would still be less than the length of the longest rope and we would still be having 84cm as the value of the median rope length.
With the assumptions above, the seven ropes would now have the lengths of the ropes as a, a, a, 84, 84, 84,(14 +4a)
summing up the values above we get 476cm which is the total length as calculated above
a + a + a +84 + 84 + 84 + 14 + 4a = 476
7a + 266 = 476
7a = 476 - 266
7a = 224
a = 30
since a = 30, we can substitute it into the equation of the longest rope (4a +14)
longest rope = (4x 30) + 14 = 134cm
