Question 1202917
.
Peter the postman was managing some letters. After mailing out 4/5 of his letters, 
he received 30 new ones. He then mailed out 1/6 of his letters and received 15 more letters. 
In the end, Peter had 70 letters.
How many letters did he have at first?
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        This problem can be solved mentally,  by using the backward method.

        The solution is accessible for a  4th - 5th grade students  that are

        unfamiliar with equations yet,  and develops their ingenuity.



<pre>
In order for the solution be clear, I present the given part in steps.

    1.  First, he mailed out 4/5 of the letters.

    2.  Then 30 new letters arrived.

    3.  Then mailed out 1/6 of his letters.

    4.  Then 15 more letters arrived.

    5.  At the end, were there 70 letters.


Solving backward, we see that immediately before step 4, were there 70-15 = 55 letters.


These 55 letters comprised 5/6 of what he had immediately before step 3.
Hence, 1/6 comprised 55/5 = 11 letter;  hence, immediately before step 3, there were 11*6 = 66 letters.


Hence, immediately before step 2, there were 66 - 30 = 36 letters.


These 36 letters comprised 1/5 of what he had at first.
Hence, at first, there there 36*5 = 180 letters.
</pre>

Solved.


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To see many other similar &nbsp;(and different) &nbsp;solved problems by the backward method, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/equations/Solving-simple-and-simplest-problems-by-the-backward-method.lesson>Solving problems by the backward method</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/equations/Solving-problems-on-the-remaining-amount.lesson>Solving more complicated problems by the backward method</A> 

in this site.


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