# I think this is a ratio problem š¬

#### Ginandtonic

##### New member
Iām struggling with my 9 year oldās maths problem Any help with method and answer much appreciated. āIn 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

#### Subhotosh Khan

##### Super Moderator
Staff member
Iām struggling with my 9 year oldās maths problem Any help with method and answer much appreciated. āIn 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
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.

#### Romsek

##### Senior Member
there will be a repeating pattern of GGBBBBB GGBBBBB and ending in GG by itself

so some number of groups of 7 and then 2 at the end sum up to 583. See if that helps

#### Dr.Peterson

##### Elite Member
āIn a line of 583 children, every 5 boys stand between 2 girls. How many boys are there?ā
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.

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.

#### pka

##### Elite Member
āIn 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
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.
With ten girls we can have forty-five boys. So for g girls we can have 5(g-1) boys.

#### JeffM

##### Elite Member
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 NOT help any student on a test.

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

#### Dr.Peterson

##### Elite Member
@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.

#### lookagain

##### Elite Member
I reported hoosie's post (post # 6) and asked for him/her to be given a warning
(meant to stop doing what he/she did).

#### hoosie

##### Junior Member
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.

#### pka

##### Elite Member
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.
First, you do not know for sure that the poster was a parent do you?
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.

#### Math a Magic

##### New member
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

Last edited by a moderator:

#### hoosie

##### Junior Member
@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.
@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 donāt wish to cause offence.

#### Ginandtonic

##### New member
Gosh - so sorry to create issues. It is in fact very helpful to have the worked method here in detail. I donāt want the answer, just the method so I can work through it with my son. I can normally figure mathsy things out by looking in books or in the internet (as Iām not a natural talent!) but I was defeated by this one! Iām very, very grateful for your help! I have no handy friends or relatives to go to. I always tell my boys they must visualise word problems, Iām a childrenās book illustrator, so we normally draw a picture. In this case we drew the two girls and five boys. It then seemed to me, logical to do multiples of seven till we hit the end target. This method fell to pieces as seven doesnāt divide nicely into the total, and we were then left with a remainder and I wasnāt sure if it would be made of girls or boys. Anyway, Iām very grateful for your help - thank you

#### Subhotosh Khan

##### Super Moderator
Staff member
Gosh - so sorry to create issues. It is in fact very helpful to have the worked method here in detail. I donāt want the answer, just the method so I can work through it with my son. I can normally figure mathsy things out by looking in books or in the internet (as Iām not a natural talent!) but I was defeated by this one! Iām very, very grateful for your help! I have no handy friends or relatives to go to. I always tell my boys they must visualise word problems, Iām a childrenās book illustrator, so we normally draw a picture. In this case we drew the two girls and five boys. It then seemed to me, logical to do multiples of seven till we hit the end target. This method fell to pieces as seven doesnāt divide nicely into the total, and we were then left with a remainder and I wasnāt sure if it would be made of girls or boys. Anyway, Iām very grateful for your help - thank you
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.

#### Ginandtonic

##### New member
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.
Will do, many thanks again.

#### Dr.Peterson

##### Elite Member
Gosh - so sorry to create issues. It is in fact very helpful to have the worked method here in detail. I donāt want the answer, just the method so I can work through it with my son. I can normally figure mathsy things out by looking in books or in the internet (as Iām not a natural talent!) but I was defeated by this one! Iām very, very grateful for your help! I have no handy friends or relatives to go to. I always tell my boys they must visualise word problems, Iām a childrenās book illustrator, so we normally draw a picture. In this case we drew the two girls and five boys. It then seemed to me, logical to do multiples of seven till we hit the end target. This method fell to pieces as seven doesnāt divide nicely into the total, and we were then left with a remainder and I wasnāt sure if it would be made of girls or boys. Anyway, Iām very grateful for your help - 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.

#### Ginandtonic

##### New member
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.
Thank you - Iām hoping now weāve got the answer to this one, Iāll 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!