SOLUTION: The camera has 10.1 million pixels. The product of the pixels across the screen times the pixels up the screen gives the number of pixels the camera has. The ratio of pixels across

Ikleyn ignores the fact that there are exceptions to the 'rounding off' rule,:
 
"Round up if first digit you're dropping is 5 or more" rule, otherwise round
down". 

One exception would be that if the question of a problem asks the number of
people that can fit into a room, and your calculation gives 11.9, the answer
would be 11 rather than 12.

The exceptions to that rule are in word problems dealing with things that we
cannot have fractions of, such as people or pixels.  We must have whole 
numbers of people and pixels.

Therefore, in this problem we must be conservative and round down the number of
pixels, for there is not enough room on the camera to squeeze in one whole extra
pixel. 

Answer: 3669, not 3670.

Also, Ikleyn frowns on the use of online technology. I see nothing wrong with it
in solving word problems, for the skill in a word problem is translating English
sentences to algebra sentences (aka equations). That is, setting up the
equations, not solving them.
  
Edwin

So, in my solution I got x = 917.4239296, 4x = 4*917.4239296 = 3669.696, and I rounded it to 3670,
                                               following standard rounding rules.

                                          3x = 3*917.4239296 = 2752.272, and I rounded it to 2752,
                                               following standard rounding rules.

Now the product (4x)*(3x) is  3670*2752 = 10099840, and it is less than 10.1 million.



So,  prevents me from claiming that 3670 is the  number of pixels across the camera.



On contrary, if I take the number 3669, then the product  (4x)*(3x)  will be 3669*2752 = 10097088,  
which means that I loose many (2752) pixels for nothing (due to using wrong conception).

Ikleyn is convinced that there are no exceptions to the "round up and down rule".
She believes it so strongly that she believes a whole pixel can fit in a space
which is only 69.6% of the room necessary for a pixel to fit. 

Edwin

PS. She was right that I accidentally typed 1010000 for 10100000, but didn't use
it in my calculation.  I corrected it.

In my previous post i PROVED that 

    - the pair (3670,2752) provides the product, i.e. the number of pixels, 
      which is less than 10.1 millions, so these dimensions fit to the problem;

    - the pair (3759,2752) provides lesser product, i.e. lesser number of pixels,
      than 10.1 millions, so we need to reject this pair;

    - the pair (3759, 2753) provides greater product, i.e. greater number of pixels
      than 10.1 millions, so we need to reject this pair, too.


Thus, I proved numerically, that my pair (3670,2752) is the best approximation for 10.1 millions pixels
from the bottom, comparing to other possible pairs, and THEREFORE this pair (3670,2752) is the UNIQUE solution
to this problem, giving 3670 as the UNIQUE possible correct answer to the problem.


The exceptions Edwin speaks in his post are irrelevant to my reasoning.
The logic of my solution overcomes his argument.


I simply showed/proved that 3670 pixel across and 2752 pixel up FIT the restriction of 10.1 million pixels
and is the best possible approximation to 10.1 million pixels in this problem.



    +----------------------------------------------------------------+
    |  My statement is that 3670 is correct answer to this problem,  |
    |                  while 3669 is not.                            |
    +----------------------------------------------------------------+



And this is all that I state. This is all that I proved.