Turn on thread page Beta
    • Thread Starter
    Offline

    13
    ReputationRep:
    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
    • Thread Starter
    Offline

    13
    ReputationRep:
    any help out there?
    Offline

    0
    ReputationRep:
    (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...
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by theone)
    Err, this is wrong...
    how?
    • Thread Starter
    Offline

    13
    ReputationRep:
    (x-1)(y+3)-17=0
    Offline

    18
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    13
    ReputationRep:
    (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?
    Offline

    0
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    13
    ReputationRep:
    (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?
    Offline

    0
    ReputationRep:
    (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...
    Offline

    18
    ReputationRep:
    (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?
    • Thread Starter
    Offline

    13
    ReputationRep:
    (Original post by theone)
    Yeah, and then work out the corresponding y-values...
    the one in bold gives y=-20
    • Thread Starter
    Offline

    13
    ReputationRep:
    (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?
    Offline

    18
    ReputationRep:
    (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...
    Offline

    18
    ReputationRep:
    Find an integer that is 11 times the sum of its digits, e.g. 63 is seven times the sum of its digits...
    • Thread Starter
    Offline

    13
    ReputationRep:
    (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?
    Offline

    15
    ReputationRep:
    (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.
    Offline

    0
    ReputationRep:
    (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.
    Offline

    18
    ReputationRep:
    (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?
    Offline

    0
    ReputationRep:
    (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
 
 
 
Turn on thread page Beta
Updated: December 1, 2003
Poll
Is the Big Bang theory correct?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.