Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ajprincess

  • one year ago

Please help:) Write 25 as sum of two positive integers one of which is divisible by 3 and other by 2.

  • This Question is Closed
  1. kewlgeek555
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay...think of the numbers that are divisible by 3 and the numbers that are divisible by two. List all the numbers until 25. Then, experiment and see which ones equal 25.

  2. ajprincess
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i knw the numbers are 15 and 10. but I want a method to find them

  3. ajprincess
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ya it certainly can be:) that's another way

  4. ajprincess
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm ya. I tried in some other way but ended with one positive and negative.

  5. ajprincess
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    25=3x+2y g.c.d(3,2)=1 3=2.1+1 2=1.2 1=3-2.1-(1) (1)*25=>25=3.25-2.25 25=3.25+2.(-25) 25=3x+2y x=25 and y=-25 25=75-50

  6. AravindG
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i think we can have many values because the equation we have is of a straight line 3x+2y=25

  7. hartnn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    25=3.25+2.(-25) 25=3x+2y ------------------------correct till here x=25+2n and y=-25 -3n now, since x,y are positive, what can you say about n ?

  8. klimenkov
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \(25=3x+2y\) (We will put a domain restriction later) \(y=\frac{25-3x}2\) All you need to find all the values of \(25-3x\) that it will be divisible by 2. Also x,y must be positive. So lets vary x: Try x=0, then y is not an integer. x=1 y=11 - good x=2 y is not an integer As we notice if x is odd we will get an integer y, and not integer in the other case. So, we have all odd positive x till the time x=9, because if x=9 y =-1 and is non-positive. The answer: x=1 y=11 x=3 y=8 x=5 y=5 x=7 y=2

  9. AravindG
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yep positive integers

  10. klimenkov
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    All you have to to is to put values from the answer into the expression for \(25=3x+2y\).

  11. hartnn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    25+2n>0 n>-25/2 ---->n>-12 as n is integer(maybe positive or negative) similarly do for y=-25 -3n yes, http://openstudy.com/users/ParthKohli#/updates/50e43ad3e4b0e36e35145cc6

  12. klimenkov
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @hartnn I think it is but it was not so difficult to notice.

  13. hartnn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    -25-3n>0 -3n >25 n<-25/3 n<-8 so 'n' takes values from -8 to -12 put values of n from -8,-9,-10,-11,-12 and get different pairs of x,y

  14. shubhamsrg
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Juts write out all odd multiples of 3 less than 25 subtract that multiple from 25, the other number will then obviously be a multiple of 2

  15. hartnn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i think -8 won't come, put n=-9,-10,-11,-12

  16. hartnn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @ajprincess following any of this ? :P ask if u have doubt in any step...

  17. ajprincess
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @hartnn I dnt get how u write x=25+2n

  18. hartnn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thats because, thats the general form x='+' 25 '+' (other co-efficient)(integer) if negative, x='-'25 '-'(other co-efficient)(integer)

  19. hartnn
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    25=3.25+2.(-25) 25=3x+2y here,for 25, other co-efficient is 2 for -25, other co-eff is 3

  20. experimentX
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3m + 2n = 25 2n = 25 - 3m, odd - odd = even, so just count odd number such that 25 - 3m > 0

  21. ajprincess
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanx a lot everyone for helping me:)

  22. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.