Help! (sum of three numbers)

[sadiamek]

Please can someone help me with this question:

Umar thinks of three numbers.
He can make three different pairs of numbers with the three numbers.
The pairs sum to 8, 15 and 17.
He says "I can work out the sum of the three numbers WITHOUT finding out what each of them is"
Explain clearly how he can do this and give the sum of the three numbers.[/color]

Thanks

[Daogroupie]

Post this in the Maths section, then you will get all the forum helping you, not just those in Herts and N London! DG

[nyr]

Let's say the numbers are a, b and c, so we have that:

a+b = 8
a+c = 15
b+c = 17

If we add these equations we get:

2a + 2b + 2c = 8+15+17 = 40

So, a+b+c = 20

nyr

[Guest55]

You don't need to use any algebra to deduce this!

[nyr]

Of course it can be done in the head in a split second but the algebra clearly explains why the answer is what it is, a requirement for a valid answer. It may also make it clearer for those less comfortable with these sorts of questions.

nyr

[Guest55]

This question is not designed for algebra; there is no need to show working in 11+ tests.

Using algebra when it is not required just over complicates the problem and confuses children.

[fiate2000]

I am with nyr on this one. Although there is no need to show workings in 11+ tests, both my DS find it easy to grasp new concepts with worked example (with algebra, diagrams, or even Lego blocks). Once they understand how it works they learn to do it in head.

Guest55 - would you care to explain how you teach this to a 10year old, so I, OP and others can benefit? "you don't need this" comment without an alternative method helps nobody.

[Guest55]

I was in a hurry so sorry for brief post but I have said before numerous times that algebra is never needed for these questions.

There are three numbers and we add them in pairs.

2 x 3 = 6 so when we add the pairs we get the total of six numbers which is double what we need.

If they can't see that then I might pick some numbers and get them to try them out so they see what happens ...

[mad?]

Sorry G55 but I don't understand that...

[sgcmum]

The sum of all the pairs is 40. But each number is included twice since you add in pairs.so you need to divide by two to get the sum of the three numbers,giving you the answer 20. Hope that helps.