Stuck on maths question

[hercules1]

Okay, got a question from the rules of maths book that I can't work out.

In a survey conducted in a junior school it was found that on one evening four times as many children watched BBC one as watched BBC2, and that twice as many children watched ITV as watch BBC one. If there were 310 children in the school, how many children watched each channel?

Any help gratefully received.

Me too!

Say that the number watching BBC2 is x.

The number watching BBC1 is four times as many, 4x.

And the number watching ITV is twice that, 4x x 2 = 8x

So all together x + 4x + 8x = 310

Simplify 13x = 310
At which point you have to dissect some children.

Could it be a misprint for 130 children in the school?

Then x=10.

So 10 watch BBC2, 40 BBC1 and 80 ITV.

ITV- 184
BBC1 - 92
BBC2 - 23

Let the number of children watching BBC1 be A, BBC2 be B and ITV be C

A = 4B

C = 2A

=> C = 8B

A + B + C = 310

=> 4B + B + 8B = 310

B = 310/ 13

Agree with Edith, is there a misprint?

It doesn't work as if
24 kids watch bbc2
96 kids watch bbc1
192 kids watch itv

Adds up to 312

Edith's right. It does not compute.

Dh and I have been trying for ages. Dd is long gone to bed! We got to the 13 parts bit and think there must be a mistake.

Yes I agree with all above its a misprint.

The number has to be divisible by 13.

Bbc1 = a
Bbc2 = b
Itv = c

a = 4b
c = 2a
c = 8b

a + b + c = 310
4b + b + 8b = 310
13b = 310

But that gives you a number for b that isn't a whole number, so either I'm wrong or the question is.

It's not a misprint. Add up all the proportions (8+4+1=13) and divide 310 by 13 and then multiply up by the proportions, so for itv, it's 13x8, for BBC1, it's 13x4 & for BBC2, it's 13x1

But you can't have .84 of a child, Pippi.

Pippi, that doesn't add up to 310 though.

pippi - 310/13 =23.846

The BBC 2 viewers cant be 1/13th. Surely?

Ah well, another ten minutes of my life I'll never get back because of school worksheet maths.

Sorry, my mistake, it's 310 Divided by 13 = 23, so for ITV is 8x23, BBC1is 4x23 and so on

We wondered whether it was something to do with not all the children watching TV but it doesn't tell you how many children didn't watch.

The trouble with that, pippibluestocking is that 310/13 = 23.85, so the pupils would need to be cut into pieces.

If 11 children were playing x-box, pippi would be very happy.

God you're right, ignore me!!

It doesn't work.

We agreed on Sunday you can't chop up children!

We don't have a people carrier so I said 2.5 DCs had to go in me and DHs cars. The assembled girls refused to oblige, 3&2 was their best offer

I suppose it could be pippi's answer, plus 11 children doing their maths homework...

Some may not have been watching tv at all & it's a sneaky question. Or a misprint.