Question 551377
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2000 students in the whole school and only 55 of 90 students are buying yearbooks approximately. 
How many books should be ordered ?
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        Tutor  @Theo solved this problem in his post,  but I came to present my solution

        and some additional thoughts about the rounding of final number.



<pre>
Similar as @Theo did in his post, you apply the ratio of 55/90 to 2000 to get 

    55/90 * 2000 = 1222.2222 students requiring books.


Formal rule says to round to 1222, but the common sense says to round to 1223.


Which way will you prefer ?  My common sense tells me to round to 1223.


Potentially, there are 1222.222 students, who want to buy yearbooks, 
and if the school wants to serve everyone of potential buyers, the school should have 1223 textbooks in the store.
</pre>

This problem illustrates that in some cases common sense &nbsp;OVERLAYS &nbsp;the formal rules.


This statement can be re-phrased in other words: &nbsp;some problems &nbsp;DICTATE &nbsp;to round 
differently than the formal rules.


It is worth to learn, &nbsp;and this problem is a good example.


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In this problem, &nbsp;a reasonable mathematical answer says that, based on given data, 
the school should order &nbsp;<U>at least</U> &nbsp;1223 &nbsp;yearbooks.



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Interesting fact:


Today, &nbsp;Oct.14, &nbsp;2025, &nbsp;I submitted this problem to &nbsp;Google &nbsp;AI &nbsp;(" Overview AI ").


It was interesting to me, &nbsp;how this &nbsp;AI &nbsp;will treat this problem.


It created the answer exactly as in the post by &nbsp;@Theo.


It is very natural, &nbsp;since &nbsp;Google &nbsp;AI &nbsp;is not able to think: &nbsp;&nbsp;it is programmed 
to rewrite from its database solutions, &nbsp;and it is all what it really can do in Math problems.


Naturally, &nbsp;1222 &nbsp;is the lame answer.


I reported to them via their feedback system.
Hope, &nbsp;in the feature, &nbsp;Google &nbsp;AI &nbsp;will be more smart, having my solution in its database.



It is why I am checking the solutions by other tutors and fix/correct them, &nbsp;when required.
Otherwise, &nbsp;thousands of students will have millions defective solutions from &nbsp;Artificial &nbsp;Intelligence,
so, &nbsp;their mind and their common sense will be injured by the &nbsp;AI,
while this &nbsp;AI &nbsp;will be beaten by the competitors.


I am a devoted partner of artificial intelligence, &nbsp;and I work tirelessly 
to ensure that the solutions to &nbsp;Math problems in its database are correct.