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1. Lo bods,

for which intergers x and y does the equation xy=20-3x+y hold?

Ive got to this stage:

(x-1)(y+3)=20

Ive worked that by subsituting x or finding y, does not work, cause ive tried and proved that 0=0
2. any help out there?
3. (Original post by 2776)
Lo bods,

for which intergers x and y does the equation xy=20-3x+y hold?

Ive got to this stage:

(x-1)(y+3)=20
Err, this is wrong...
4. (Original post by theone)
Err, this is wrong...
how?
5. (x-1)(y+3)-17=0
6. (Original post by 2776)
Lo bods,

for which intergers x and y does the equation xy=20-3x+y hold?

Ive got to this stage:

(x-1)(y+3)=20

Ive worked that by subsituting x or finding y, does not work, cause ive tried and proved that 0=0
xy=20-3x+y
3x+xy-y=20
(x-1)(3+y)+3=20
(x-1)(3+y)=17

After reading theone's post I thought I'd try and take it as far as I can and this is it.
7. (Original post by ZJuwelH)
xy=20-3x+y
3x+xy-y=20
(x-1)(3+y)+3=20
(x-1)(3+y)=17

After reading theone's post I thought I'd try and take it as far as I can and this is it.
Yep but how do u find x or y?
8. (Original post by ZJuwelH)
xy=20-3x+y
3x+xy-y=20
(x-1)(3+y)+3=20
(x-1)(3+y)=17

After reading theone's post I thought I'd try and take it as far as I can and this is it.
To continue...

since x-1 and y+3 must both be integers and since 17 = 17.1 or -17.-1 x-1 to one of these four factors. So set x-1 = 17,1,-1 and -17 and work out x then y.
9. (Original post by theone)
To continue...

since x-1 and y+3 must both be integers and since 17 = 17.1 or -17.-1 x-1 to one of these four factors. So set x-1 = 17,1,-1 and -17 and work out x then y.
so like this:

x-1 = 17
x-1 = 1
x-1 = -1
x-1 = -17?
10. (Original post by 2776)
so like this:

x-1 = 17
x-1 = 1
x-1 = -1
x-1 = -17?
Yeah, and then work out the corresponding y-values...
11. (Original post by 2776)
so like this:

x-1 = 17
x-1 = 1
x-1 = -1
x-1 = -17?
The one in bold returns no answer I think.

So do you go on to do the same to y?
12. (Original post by theone)
Yeah, and then work out the corresponding y-values...
the one in bold gives y=-20
13. (Original post by theone)
Yeah, and then work out the corresponding y-values...
Right another problem thats bugging me:

Find all positive intergers which are equal to 11 times the sum of their digits.

I don't actually get the question itself. Is it telling me to find the 11 times the sum of an interger?
14. (Original post by 2776)
Right another problem thats bugging me:

Find all positive intergers which are equal to 11 times the sum of their digits.

I don't actually get the question itself. Is it telling me to find the 11 times the sum of an interger?
You're doing the prep questions for the BMO aren't you? I knew I saw that last question before...
15. Find an integer that is 11 times the sum of its digits, e.g. 63 is seven times the sum of its digits...
16. (Original post by ZJuwelH)
You're doing the prep questions for the BMO aren't you? I knew I saw that last question before...
yep, but dont know where to start. what is the question asking me?
17. (Original post by 2776)
yep, but dont know where to start. what is the question asking me?
in the number ab, the sum of its digits is a+b, the actual number is 10a + b, so 10a + b = 11(a+b)

a + 10b = 0

so there are no 2 digit numbers that satisfy you question.

but this might not be the case for 3+ digits, haven't checked.
18. (Original post by 2776)
yep, but dont know where to start. what is the question asking me?
You have to start by proving you can only do this when the number in question is a 3 digit number. Then let n (the 3 digit number) = 100a + 10b + c where a,b,c are integers <10 and then set that equal to 11(a+b+c) (i.e. 11 times the sum of their digits)
Let me know if you're stuck again.
19. (Original post by elpaw)
in the number ab, the sum of its digits is a+b, the actual number is 10a + b, so 10a + b = 11(a+b)

a + 10b = 0

so there are no 2 digit numbers that satisfy you question.

but this might not be the case for 3+ digits, haven't checked.
I get the gist of this but the step in bold, where's it from and what's it mean?
20. (Original post by ZJuwelH)
I get the gist of this but the step in bold, where's it from and what's it mean?
From subtracting 10a + b = 11a + 11b

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