SOLUTION: 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 t

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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 t      Log On


   

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?
Found 4 solutions by ankor@dixie-net.com, MathTherapy, ikleyn, papachick24025:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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?
;
let x = no. of letters originally
5%2F6(x - 4%2F5x + 30) + 15 = 70
since he mailed out 1/6 of this total he had 5/6 left
5/6 times 4/5 = 2/3 and 5/6 times30 is 25
5%2F6x - 2%2F3x + 25 = 70 - 15
5%2F6x - 4%2F6x + 25 = 55
1%2F6x = 55 - 25
1%2F6x = 30
x = 6*30
x = 180 originally


Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
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?

Let original number of letters be L
After mailing out 4%2F5 and then receiving 30 new, he then had matrix%281%2C5%2C+1%2F5%2C+of%2C+%22L+%2B+30%2C%22%2C+or%2C+L%2F5+%2B+30%29 

After mailing out 1%2F6 of L%2F5+%2B+30. he then had  

Since after receiving 15 more, the final count amounted to 70, we then get: 
                                                Original number of letters, or L = 180

Answer by ikleyn(52908) About Me  (Show Source):
You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~


        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. 


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.

Solved.

--------------------

To see many other similar  (and different)  solved problems by the backward method,  look into the lessons
    - Solving problems by the backward method
    - Solving more complicated problems by the backward method
in this site.

Consider these lessons as your textbook,  handbook,  tutorials and free of charge home teacher,  which is always with you.

Practice and learn the method from these lessons.



Answer by papachick24025(6) About Me  (Show Source):
You can put this solution on YOUR website!
Peter had 4/5 of his letters left after mailing out some of them. 4/5 of 70 is 56.
He then received 30 more letters, bringing his total to 86.
He then mailed out 1/6 of his letters, leaving him with 7/6 of 86, or 70.
He then received 15 more letters, bringing his total to 70.
Therefore, he had 86 letters before receiving the 15 letters, and 86 - 70 = 16.
Therefore, he had 16 + 70 = 86 letters before receiving the 15 letters.
Therefore, he had 86 + 30 = 116 letters before mailing out 1/6 of them.
Therefore, he had 116 + 56 = 172 letters before mailing out 4/5 of them.
Therefore, he had 172 + 8 = 180 letters at first.