A box has 40 balls with a weight of 30 g, 20 with a weight of 50 g and 10 that weigh 100 g. What is the average weight of a ball in the box.Why is it not 60 g.
The box has 40 balls with a mass of 30 g, 20 with a mass of 50 g and 10 that have a mass 100 g each. If the number of balls with each of the given mass was the same, the average mass of the balls would indeed have been `(30 + 50 + 100)/3 = 60 g` .
But the number of balls with each of the given mass is not the same. There are a total of 40 balls that have a mass of only 30 g, the number of balls of 50 g and 100 g is 20 and 10 each. To find the average mass of each ball in the box, first determine the total mass of all the balls in the box and divide it by the total number of balls.
The mass of all the balls is 40*30 + 20*50 + 10*100 = 1200 + 1000 + 1000 = 3200 g. The total number of balls in the box is 40 + 20 + 10 = 70.
This gives the average mass of each ball as `3200/70 ~~ 45.71` g
The average mass of each ball in the box is approximately 45.71 g