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I don't want algebraic solution to this question as i already have it.. as i have to teach it to a student with no algebra knowledge.

There are 42 pupils in a class. 3/4 of the boys and 2/3 of the girls travel to school by bus. The total number of boys and girls who travel to school by bus is 30. How many boys are there in the class? How many girls travel to school by bus?

Adi Dani
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Tasawar Hussain
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  • i have an answer like this https://answers.yahoo.com/question/index?qid=20100830211359AAtY1D5 ...but as i said i dont want algebric solution to this question. – Tasawar Hussain Oct 16 '16 at 11:17
  • Why do you have to teach this particular problem to that particular student? Suppose there isn't any way to solve it without algebra – what do you do then? Some problems are not meant to be given to people who have no algebra. – Gerry Myerson Oct 16 '16 at 12:12
  • this question is picked from oxford book. And it is in the chapter with concept of rational numbers only. – Tasawar Hussain Oct 17 '16 at 14:22

1 Answers1

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The fact that we can assume that there are a non-negative, integer number of both boys and girls makes this a finite problem. That is, we could in principle check every possible case by hand. We can reduce our task if we make a couple of basic observations:

$B$, the number of boys, must be divisible by $4$. If we list the pairs $(B,G)$ we get $$(4,38),(8,34),(12,30),(16,26),(20,22),(24,18),(28,14),(32,10),(36,6),(40,2)$$ SImilarly, $G$ must be divisible by $3$ and we see that only $(12,30),(24,18),(36,6)$ are candidates. And it is easy to check that only $\boxed {(24,18)}$ gets the job done.

You can speed this up by remarking that, since $42$ and $G$ are both divisible by $3$ then $B$ must be as well. Hence $B$ is divisible by $12$ so we get down to three cases instantly.

lulu
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