SOLUTION: The traveler account 96 layers in the stack (so the bottom layer has 96 pipes) The traveler pays $ .12 Per pound of scrap metal and estimates that each pipe weighs 8 pounds. (1 pi

Question 1181352: The traveler account 96 layers in the stack (so the bottom layer has 96 pipes) The traveler pays $ .12 Per pound of scrap metal and estimates that each pipe weighs 8 pounds.
(1 pipe on top, 2 pipes in the second, 3 pipes on the third layer and so on)
How many total pipes are in the stack?
How much does a traveler offer to pay for all the pipes?
Answer by ikleyn(52898) (Show Source): You can put this solution on YOUR website!
.


The number of pipes is this sum

    1 + 2 + 3 + 4 + . . . + 96.      (*)


It is the sum of the first 96 natural numbers (arithmetic progression).


It is well known fact that the sum of the first "n" natural numbers is equal to  .


So, in your case the sum of the numbers (*) is equal to   = 4656.



The last step in solution of this problem is to multiply the found number of pipes  4656  by 8 and by 0.12  
to get the answer in dollars.


I leave it to you to complete this simple calculation.

Have fun (!)

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

For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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