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 Post subject: Maths Question Consortium 2008 Q30Posted: Sun Dec 15, 2013 3:13 pm

Joined: Sat Dec 08, 2012 6:17 pm
Posts: 22
Completely stumped. From the Godolphin and Latymer website:

AB and C represent different digits.

AB + C =50

BC + A = 41

What are the values of A, B and C?

Yikes. This is tricky. Any suggestions how to tackle.

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 Post subject: Re: Maths Question Consortium 2008 Q30Posted: Sun Dec 15, 2013 3:45 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11934
A,B and C are digits .... think about that.

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 Post subject: Re: Maths Question Consortium 2008 Q30Posted: Sun Dec 15, 2013 5:22 pm

Joined: Sat Dec 08, 2012 6:17 pm
Posts: 22
I have just realised how easy this is. I thought the first two 'digits' were to be multiplied first. Doh!

Thanks anyhow for looking

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 Post subject: Re: Maths Question Consortium 2008 Q30Posted: Sun Dec 15, 2013 5:36 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11934
That's why I only gave a hint!

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 Post subject: Re: Maths Question Consortium 2008 Q30Posted: Mon Dec 16, 2013 11:11 am

Joined: Fri Oct 11, 2013 8:55 am
Posts: 500
10A + B + C = 50 (1)
10B + C + A = 41 (2)

(1) - (2) 9A - 9B = 9

A = B + 1

So substituting this in (2) gives:

10B + C + B + 1 = 41
11B + C = 40

Since C is a single digit the only value B can have is 3.

Therefore, C = 7

And A = 4.

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 Post subject: Re: Maths Question Consortium 2008 Q30Posted: Mon Dec 16, 2013 1:56 pm

Joined: Mon Aug 22, 2011 8:20 pm
Posts: 1706
Location: Warwickshire
It is simpler than that:
AB + C =50 C can't be more than 9 so A must be 4 (and B+C must be 10 although you don't need that fact)

BC + A = 41 given A is 4, BC must be 37 so B is 3 and C is 7

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 Post subject: Re: Maths Question Consortium 2008 Q30Posted: Mon Dec 16, 2013 2:01 pm

Joined: Fri Oct 11, 2013 8:55 am
Posts: 500
Okanagan wrote:
It is simpler than that:
AB + C =50 C can't be more than 9 so A must be 4 (and B+C must be 10 although you don't need that fact)

BC + A = 41 given A is 4, BC must be 37 so B is 3 and C is 7

Yeah, you're right. I over complicated it a bit!

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