SOLUTION: The average of the six lights was 100 pounds. The average weight of the ten mediums was 140 pounds, and the average weight of the four heavies was 180 pounds. What is the overall a

Hi, there--

The Problem:
The average of the six lights was 100 pounds. The average weight of the ten mediums was 
140 pounds, and the average weight of the four heavies was 180 pounds. What is the overall 
average?

A Solution:

We can work backwards to figure this out. We find the average of a set of numbers by adding them 
and dividing their sum by how many numbers there are.

We have six lights. Their average is 100 pounds. Working backwards, the sum of the lights must 
be 600 pounds. (We would divide the sum 600 by 6 to get the average 100.)

We have ten mediums. Their average is 140 pounds, so the sum of the mediums must be 840 
pounds (140*6=840).

We have four heavies. Their average is 180 pounds. The sum of the heavies must be 720
pounds because (you guessed it...4*180=720.)

To get the overall average, we need to add up all the weights and divide by the number of items.
The sum of all the lights + the mediums + the heavies is 600 + 840 + 720 = 2160 pounds.

Altogether, there are 6 + 10 + 4 = 20 items.

Therefore the overall average is 2160/20 = 108 pounds.

Feel free to email me if you have questions about the solution. I'd appreciate any feedback you 
have to offer.

Ms.Figgy
math.in.the.vortex@gmail.com