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- ajprincess

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

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- ajprincess

- katieb

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- 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

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

- ajprincess

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

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- ajprincess

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

- 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

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

- 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

\(25=3x+2y\)
(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

yep positive integers

- klimenkov

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

- 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

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

- 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

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

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

- hartnn

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

- ajprincess

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

- hartnn

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

- 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

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

- ajprincess

Thanx a lot everyone for helping me:)

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