SOLUTION: I am thinking of more than one number. If you add 1 to my numbers and then multiply them by 5 you will get multiples of 5 between 40 and 65. What are the numbers that I am thinkin

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Question 1197175: I am thinking of more than one number. If you add 1 to my numbers and
then multiply them by 5 you will get multiples of 5 between 40 and 65. What are the numbers that I am thinking of?
Found 3 solutions by greenestamps, math_tutor2020, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Your number: n

1 added to your number: n+1

That number multiplied by 5: 5(n+1)

The resulting number is a multiple of 5 between 40 and 65:

40 < 5(n+1) < 65
8 < n+1 < 13
7 < n < 12

Since the number you ended up with was a multiple of 5, the original number n had to be an integer. So the numbers you are thinking of are the integers between 7 and 12.

ANSWER: Your numbers are 8, 9, 10, and 11.

NOTE: "between 40 and 65" in the statement of the problem is ambiguous; we don't know whether or not 40 and 65 are included. My interpretation is that they are not....
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

A supplement to the answer @greenestamps provided:

If you include each endpoint, then solves to which means your potential number is either 7, 8, 9, 10, 11, or 12. I agree that the term "between" is ambiguous.

Example:
Let's say your number was 8
Add 1 to get 8+1 = 9
Multiply by 5 to get 9*5 = 45
This fits the criteria since it's between 40 and 65
Answer by ikleyn(52792)   (Show Source): You can put this solution on YOUR website!
.

            Usually, even young students of the  4-th grade level can solve such problems using a backward method
            and making inverse operations in the inverse order. 

Solving this way, you make two steps:


    (1)  You divide 40 and 65 by 5, and you conclude that your numbers are integer numbers between 8 and 13.


    (2)  Then the next and the last step is to subtract 1 from the numbers, obtained in step (1).

         Doing it, you conclude that your original numbers are integer numbers between  8-1 = 7  and  13-1 = 12.



ANSWER.  Thus you found out that the original numbers are integer numbers between 7 and 12.

Solved for the  4-th grade level without using equations,  with full explanations.



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