Dhruv D.

asked • 03/12/17

The product of four consecutive natural numbers which are multiples of five is 15,000. Find the numbers.

What will be the five consecutive natural numbers for the above question??

Andrew M.

You went from stating the product of four consecutive natural numbers
to asking what will be the five consecutive numbers....
 
 
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03/12/17

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Andrew M. answered • 03/12/17

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Let your first number be 5x
The second is 5x +5
The third 5x+10
The fourth 5x + 15
 
5x(5x+5)(5x+10)(5x+15) = 15000
 
Noting that we are taking the product of 4 numbers,
which will become large quickly, we should estimate
the numbers are individually pretty small.  The 1st
natural number that is a multiple of 5 is 5. 
The easiest way to look at this is to simply say
"What if my 1st number is 5?"
 
5(10)(15)(20) = 15,000    and there's the answer.
 
Note:  If we solved out the long polynomial equation
we would have determined that x=1 and the first
number, 5x=5
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Dhruv D.

Thank you so much Sir...
 
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03/12/17

David W.

At some point, one must decipher the intent of the problem.  "Just getting the answer" is obviously not it.  It must be that learning the process -- the definitions, the rules, and the applications to life -- are the reason that many math problems are contrived.
 
For this problem, I realized that 15,000 is not huge and typed 5, 10, 15, 20, and 25 into MS Excel and then created and copied a formula for multiplying groups of four of those numbers.  Thus --
    5        15000
  10        75000
  15      225000
  20      525000
  25    1050000
 
Just finding the answer is super easy!
 
Now, multiplying (x)(X+5)(x+10)(x+15) and similar expressions by hand, at least a few times, has some little value.
 
So, perhaps a better problem would be:
   The product of four consecutive odd numbers is 2070705.  What are the four numbers?
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03/13/17

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