Question

Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. What is the maximum possible weight, in kilograms, of the lightest box? 1 2 3 4 5 Next Previous HelpEnd Review Review Screen

Answer 1

Answer: The maximum possible weight of the lightest box would be 3.

Step-by-step explanation:

Since we have given that

Average of three boxes = 7

Let the weights of three boxes be 'x', 'y', 'z'.

So, we get

$\dfrac{x+y+z}{3}=7\\\\x+y+z=7\times 3=21$

Median = 9

Since it has odd number of boxes i.e. 3

So, median would be the middle term i.e. b = 9

So, it becomes

a,9,c

Suppose c at its highest i.e. c= 9

Then it becomes,

$a+9+9=21\\\\a+18=21\\\\a=21-18\\\\a=3$

Hence, the maximum possible weight of the lightest box would be 3.