#### Ginandtonic

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- Thread starter Ginandtonic
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Please let the student contact us directly - including a copy of the "attempts to solve" for us to look-through. That will give us an idea about where we should start explaining.

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I suspect a major issue may be the interpretation of the problem. In addition, it's important to approach a problem starting with its meaning, not with an expected "tool" to be used to solve it.āIn a line of 583 children, every 5 boys stand between 2 girls. How many boys are there?ā

So I'd start by thinking about what it means, which is a little ambiguous. We can start with this:

GBBBBBG

That's 5 boys between 2 girls.

Now, how do we continue? That's where we might disagree, but I think it is meant to look like this:

GBBBBBGBBBBBGBBBBBG

So we alternate 5 boys and 1 girl (not 2, as you may have been thinking). And there will be a girl at each end, which disrupts things a bit.

(I notice I disagree with Romsek; we can argue about that, if you wish, but my plan from the start was to see if my interpretation led to a reasonable answer - it does - and then try another if it didn't.)

I'm going to leave it there, with nothing but an interpretation. See what you can do with that, and write back showing us what methods you've tried (and how you are interpreting the problem now). I could suggest some specific things to do, but those are learned best if you (that is, the child) can figure them out for yourselves.

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Consider 10 girls. G___G___G___G___G___G___G___G___G___G. Those ten girls create nine places to put five boys in each place.āIn a line of 583 children, every 5 boys stand between 2 girls. How many boys are there?ā This has bought me close to tears this evening

With ten girls we can have forty-five boys. So for g girls we can have 5(g-1) boys.

Hoosie, please stop it. Tutors are not here to show off by giving answers, but rather to help students learn how to solve problems themselves. Your giving them answers will

There are rare instances where a complete answer is appropriate, but those are indeed rare instances.

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First, you do not know for sure that the poster was a parent do you?Thought this might be an exception because the question was posed by a parent on behalf of their child. Hopefully the parent will work through the solution step by step with their son or daughter.

Even if it were, how much better for whomever to find the solution so that the explanation becomes a teaching moment.

I think that giving uncalled for full solutions is a serious offence.

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This is a pattern question and to solve this, we need to identify the pattern. Here is the pattern:

GBBBBB GBBBBB GBBBBB ... likewise. This means, in the pattern of 6 people there is 1 girl and 5 boys. We have a line of 583, since the pattern repeats itself after every 6, we need to divide 583 by 6, so we get 97 R1. Now R1 (Remainder 1) falls in next pattern which is the girl. So the same pattern repeats 97 times and in each pattern, there are 5 boys, so multiply 97 times 5 to get the total number of boys. Which is 485.

583/6 = 97 R 1

97*5 = 485

GBBBBB GBBBBB GBBBBB ... likewise. This means, in the pattern of 6 people there is 1 girl and 5 boys. We have a line of 583, since the pattern repeats itself after every 6, we need to divide 583 by 6, so we get 97 R1. Now R1 (Remainder 1) falls in next pattern which is the girl. So the same pattern repeats 97 times and in each pattern, there are 5 boys, so multiply 97 times 5 to get the total number of boys. Which is 485.

583/6 = 97 R 1

97*5 = 485

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@Dr.Peterson, my apologies. I realise I am new here (in terms of post numbers) and still learning the ropes. I suppose I was responding to the distress of the parent and forgot to apply the usual rule of not providing a full solution. Instead I should have responded to the help already provided. I enjoy being part of the forum and donāt wish to cause offence.@hoosie, I very intentionally left some ideas to be discovered, and said why. Why must you give them the complete answer???

There are several very good ways to solve this; yours is not the clearest. But the one they discover is the best.

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However, in the future please let your son ask us the questions (under your supervision) and provide his work - so that we know where to begin to help him.

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Will do, many thanks again.However, in the future please let your son ask us the questions (under your supervision) and provide his work - so that we know where to begin to help him.

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It sounds like I was correct that the main issue was a misinterpretation of the problem.

My next hint would have been to point out that there are groups of 6, with one extra girl at the far end; that would probably have been enough to get you to the answer, using a modification of what you were already thinking: subtract 1 from 583 and divide by 6 to get the number of groups of boys.

This technique is actually one I use in real life fairly often; for example, it occurs in arranging pictures on a wall with equal spaces between them and at each end, or in counting sections of fencing separated by posts.

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Thank you - Iām hoping now weāve got the answer to this one, Iāll be more familiar with the whole thing if he gets another similar question. And yes! Might be handy in real life too (and much more accurate than my normal method of doing it by eye!) Thank you!It sounds like I was correct that the main issue was a misinterpretation of the problem.

My next hint would have been to point out that there are groups of 6, with one extra girl at the far end; that would probably have been enough to get you to the answer, using a modification of what you were already thinking: subtract 1 from 583 and divide by 6 to get the number of groups of boys.

This technique is actually one I use in real life fairly often; for example, it occurs in arranging pictures on a wall with equal spaces between them and at each end, or in counting sections of fencing separated by posts.