ajprincess
  • ajprincess
Please help:) Write 25 as sum of two positive integers one of which is divisible by 3 and other by 2.
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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kewlgeek555
  • kewlgeek555
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.
ajprincess
  • ajprincess
i knw the numbers are 15 and 10. but I want a method to find them
ajprincess
  • ajprincess
ya it certainly can be:) that's another way

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ajprincess
  • ajprincess
hmm ya. I tried in some other way but ended with one positive and negative.
ajprincess
  • ajprincess
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
AravindG
  • AravindG
i think we can have many values because the equation we have is of a straight line 3x+2y=25
hartnn
  • hartnn
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 ?
klimenkov
  • klimenkov
\(25=3x+2y\) (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
AravindG
  • AravindG
yep positive integers
klimenkov
  • klimenkov
All you have to to is to put values from the answer into the expression for \(25=3x+2y\).
hartnn
  • hartnn
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
klimenkov
  • klimenkov
@hartnn I think it is but it was not so difficult to notice.
hartnn
  • hartnn
-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
shubhamsrg
  • shubhamsrg
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
hartnn
  • hartnn
i think -8 won't come, put n=-9,-10,-11,-12
hartnn
  • hartnn
@ajprincess following any of this ? :P ask if u have doubt in any step...
ajprincess
  • ajprincess
@hartnn I dnt get how u write x=25+2n
hartnn
  • hartnn
thats because, thats the general form x='+' 25 '+' (other co-efficient)(integer) if negative, x='-'25 '-'(other co-efficient)(integer)
hartnn
  • hartnn
25=3.25+2.(-25) 25=3x+2y here,for 25, other co-efficient is 2 for -25, other co-eff is 3
experimentX
  • experimentX
3m + 2n = 25 2n = 25 - 3m, odd - odd = even, so just count odd number such that 25 - 3m > 0
ajprincess
  • ajprincess
Thanx a lot everyone for helping me:)

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