Alex used the method of Archimedes to determine the volume of some twigs he was using in an experiment. The class was comparing the densities of different kinds of wood. He measured the volume of 10 twigs and found the average volume was 3.1 ml. Before he completed the calculations, he discarded one measurement because he thought the twig was the wrong species. After discarding the twig he obtained, the new average volume was 2.6 ml. What must have been the volume of the twig he discarded?
To solve the problem, we can use the formula for calculating the average:
average = sum of values / number of values
Let's denote the volume of the twig Alex discarded as x. Then we can set up two equations based on the given information:
(1) (sum of volumes including x) / 10 = 3.1
(2) (sum of volumes without x) / 9 = 2.6
Multiplying both sides of equation (1) by 10, we get:
sum of volumes including x = 31
Multiplying both sides of equation (2) by 9, we get:
sum of volumes without x = 23.4
Subtracting equation (2) from equation (1), we can eliminate the sum of volumes and get:
x = sum of volumes including x - sum of volumes without x
x = 31 - 23.4
x = 7.6
Therefore, the volume of the twig Alex discarded was 7.6 ml.