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Most of you sent us the right answer to the
first question of the problem ('How many of 3kg and 8kg weights
would you need for the average (mean) of the weights to be 6kg?').
Some found it by trial and error, for example, Ellen from
It is all about trial and error. I thought I had the answer when I
had fourof 3kg weights and threeof 8kg weights. But then I noticed
that I had seven weights. Then I kept my three of 8kg which is 24kg
and all I had to do was add 2 of 3kg weights. And I had my
3 x 8kg + 2 x 3kg =30, and 30/5 = 6kg.
Andy (Garden International School) pointed
The weight averages are from 3 to 8
Rosie from St Bartholomew's Cof E Primary
School gave us the answers to some whole-number averages in between
3 and 8:
For an average of 7, you would need 4 of 8kg weights and 1 of 3kg
For an average of 6, you would need 9 of 8kg weights and 6 of 3kg
For an average of 5, you would need 2 of 8kg weights and 3 of 3kg
A general solution was provided by Hyeon
(British School Muscat):
Imagine that the lighter weight is a and the heavier weight is
As long as a < b, the smallest average you can get is a and the
biggest average you can get is b.
It is possible to get every single number in between. There are
Hyeon also noticed something important from
the results of her trial with different weights:
If the total number of averages is odd, then 1 of a and 1 of b
would give the middle average weight.
The amount of a and the amount of b used should add up to a factor
or a multiple of the difference between a and b for the average to
be a whole number.
Here are some of her trials:
For the 1kg and 5 kg weights
For the 17 kg and 57 kg weights
|Although we received many answers to
this problem, most of the answers simply stated the results rather
than providing a general strategy for finding them. However,
Anurag, from Queen Elizabeth's Grammar School in Horncastle, did
draw some general conclusions. You can see his working