Help please - pens and pencils question.

[MCLC]

I buy some pens and pencils. The total cost is 84p. The pens cost twice as much as the pencils and I buy 7 pens. How much do the pencils cost?

I know the answer (came with answers) but I don't know how to get to it.

Thanks!

[Guest55]

I buy some pens and pencils. The total cost is 84p. The pens cost twice as much as the pencils and I buy 7 pens. How much do the pencils cost?

Lots of approaches - let's try without algebra first.

Let's say pens cost 10p [cost has to be an even number]
cost = 7 x 10 = 70p
so 84 -70 = 14 but that doesn't divide by 5p.

Try pen is 8p
cost = 7 x 8 = 56p
so 84 - 56 = 28p which is divisible by 4 - so pencils cost 4p [how unrealistic!]

If we try to use algebra - let cost of pen be 2n

7 x 2n = 14n
84 - 14n = 7(12 - 2n) which has to be divisible by n ....not sure that really helps most children.

[MCLC]

Thanks Guest55!

Would you discourage the use of Algebra for such a question or encourage it?

[Guest55]

I'd discourage it as it seems to make it harder.

However a student has got to start by looking at the numbers to realise that the cost must be small ie total is only 84p.

[MCLC]

Thank you!

[Surferfish]

By my reckoning there is more than one possible correct answer to this question (which makes it a very bad question IMO as it implies that there is only a single correct answer).

Pencils could cost either 1p, 2p, 3p or 4p. (And pens would therefore cost either 2p, 4p, 6p or 8p)

To prove by algebra, if c = cost of pencil in pence and n = number of pencils,

(7x2)c + nc = 84
14c + nc = 84
(14 + n) c = 84

So (14+n) just needs to be a factor of 84 (greater than 14) which has a number of possibilities: 84, 42, 28, 21

So c could equal 1p, and number of pencils would equal 70.
c could equal 2p, and number of pencils would equal 28
c could equal 3p, and number of pencils would equal 14
c could equal 4p, and number of pencils would equal 7.

So 4 possible valid answers! Presumably the one it gives as the "correct" one is 4p (as shown by Guest55) but how is that any more correct than the others?

[RedPanda]

Was it multiple choice MCLC? That's the only way it would make sense.

There is one like this in the GL packs (can't remember which test) where the question on its own doesn't make sense. You had to work back from the answers. Check which answer would work so to speak.

[MCLC]

Yes it was a multiple choice RedPanda. Not from the GL packs but a free paper I found online.

[Guest55]

It is poorly written and I loathe unreliastic prices anyway.

I went for the 4p solution because it says 'some' and the '1p' solution involves buying 70 pencils!

[MCLC]

Yes I thought it was quite an odd question as did DD.