How many of the pupils were boys?

[chijioke]

The ratio of girls to boys in a mixed school is 5:6. On a rainy day 1/6 of the girls and 1/4 of the boys were absent. If the total number pupils present that day was 390, how how many of the pupils were boys?

How do I go about this problem?
This is what I did.
Fraction of girls present is [math]1- \frac{1}{6}=\frac{5}{6}[/math]Fraction of boys present is [math]1- \frac{1}{4}=\frac{3}{4}[/math]I am stuck. How do relate fraction of girls and boys present to 390?

 

[Dr.Peterson]

The ratio of girls to boys in a mixed school is 5:6. On a rainy day 1/6 of the girls and 1/4 of the boys were absent. If the total number pupils present that day was 390, how how many of the pupils were boys?

How do I go about this problem?
This is what I did.
Fraction of girls present is [math]1- \frac{1}{6}=\frac{5}{6}[/math]Fraction of boys present is [math]1- \frac{1}{4}=\frac{3}{4}[/math]I am stuck. How do relate fraction of girls and boys present to 390?

Try defining a variable or two.

Suppose that the (total) number of boys in the school is B. What is the total number of girls?

Then, how many boys, and how many girls, are present on this day? Use those expressions to write an equation saying the total is 390/

 

[The Highlander]

The ratio of girls to boys in a mixed school is 5:6. On a rainy day 1/6 of the girls and 1/4 of the boys were absent. If the total number pupils present that day was 390, how how many of the pupils were boys?

How do I go about this problem?
This is what I did.
Fraction of girls present is [math]1- \frac{1}{6}=\frac{5}{6}[/math]Fraction of boys present is [math]1- \frac{1}{4}=\frac{3}{4}[/math]I am stuck. How do relate fraction of girls and boys present to 390?

You have done this kind of thing before, you're just not thinking it through clearly...

You could, indeed, set up expressions involving the numbers of boys & girls or you could just attack it in tiny steps using techniques that you have already shown you know how to handle.

I would suggest approaching it by defining the starting position as just, T, the total number of pupils (of both sexes) in the school. (Note that you are not given that number, you are just given the number of pupils present on the rainy day.)

Now the ratio girls:boys is given as 5:6, so what fraction of T is female and what fraction of T is male?
You've done that before, they're 11ths, aren't they (because: 5 + 6 = 11).

But a quarter of the boys are absent, so what is a quarter of \(\displaystyle \frac{6}{11}\)?

And (for the missing girls) what is a sixth of \(\displaystyle \frac{5}{11}\)?

Adding those two results together gives you the fraction of T that is absent that day, so you can then easily find out what fraction of T are present which equates to the 390 who are not absent (and, from there, the number, T, itself).

By now you have all the relevant information necessary to answer just about any question posed but it looks (to me) like the question is somewhat ambiguous (the way you have quoted it).

It looks like the question requires you to determine how many boys were present on this rainy day (when only ¾ of all the boys in the school were there) but I suspect that what they actually expect you to calculate is the total number of boys in the school as a whole.

Why? Because whoever wrote the question didn't choose their numbers carefully enough (even if the actual text of the question specifically does state that it's the total number of boys enrolled in the school that you are to find)!

Given the numbers provided, if you try to calculate the individual numbers of girls and/or boys present or absent on the rainy day, you end up with half pupils (which isn't possible with discrete data like human beings! )

Hope that helps.

 

[chijioke]

You have done this kind of thing before, you're just not thinking it through clearly...

You could, indeed, set up expressions involving the numbers of boys & girls or you could just attack it in tiny steps using techniques that you have already shown you know how to handle.

I would suggest approaching it by defining the starting position as just, T, the total number of pupils (of both sexes) in the school. (Note that you are not given that number, you are just given the number of pupils present on the rainy day.)

Now the ratio girls:boys is given as 5:6, so what fraction of T is female and what fraction of T is male?
You've done that before, they're 11ths, aren't they (because: 5 + 6 = 11).

But a quarter of the boys are absent, so what is a quarter of \(\displaystyle \frac{6}{11}\)?

And (for the missing girls) what is a sixth of \(\displaystyle \frac{5}{11}\)?

Adding those two results together gives you the fraction of T that is absent that day, so you can then easily find out what fraction of T are present which equates to the 390 who are not absent (and, from there, the number, T, itself).

By now you have all the relevant information necessary to answer just about any question posed but it looks (to me) like the question is somewhat ambiguous (the way you have quoted it).

It looks like the question requires you to determine how many boys were present on this rainy day (when only ¾ of all the boys in the school were there) but I suspect that what they actually expect you to calculate is the total number of boys in the school as a whole.

Why? Because whoever wrote the question didn't choose their numbers carefully enough (even if the actual text of the question specifically does state that it's the total number of boys enrolled in the school that you are to find)!

Given the numbers provided, if you try to calculate the individual numbers of girls and/or boys present or absent on the rainy day, you end up with half pupils (which isn't possible with discrete data like human beings! )

Hope that helps.

Try defining a variable or two.

Suppose that the (total) number of boys in the school is B. What is the total number of girls?

Then, how many boys, and how many girls, are present on this day? Use those expressions to write an equation saying the total is 390/

View attachment 1715563118331.png

 

[The Highlander]

View attachment 37842

Your answer is the same as what I would have said.

So the question did ask for the total number of boys enrolled in the school?
(Not just the number of boys present on the rainy day)

You said in your OP: "If the total number pupils present that day was 390, how how many of the pupils were boys?" which implies that the answer required is the number of boys present on that particular day.

Do you see why I was concerned about that?

​

 

[chijioke]

Can the problem be solved using another method?

 

[The Highlander]

Can the problem be solved using another method?

I'm sorry if the question I asked at the end of my previous post caused you any confusion.

I didn't man that I was concerned about the way you solved it. There are almost always other methods that can be used to solve problems like this but there was nothing wrong with your method.

I just wondered if you could see why (although the question, as it was phrased in your OP, appeared to ask how many boys were present on the rainy day) the only sensible answer that could be asked for was the total number of boys enrolled in the school (not just the number of boys present on the rainy day).

I was simply trying to draw attention to the fact that the question had been poorly constructed (because it wasn't possible for ¼ of the boys or ⅙ of the girls to be absent on any day!).

The method you chose to use wasn't very far removed from what I suggested at Post #3 and I can't think of any method that doesn't involve the use of fractions but the arithmetic in the method shown below is slightly shorter (and a bit more elegant?)...

An Alternative Method:
If the ratio of girls to boys is 5:6 then you could split all the pupils into groups of 11 (each containing 5 girls & 6 boys) and, since we are dealing with discrete data (ie: whole boys & whole girls; you can't get fractions of people) then you would end up with a whole number of groups. (Basically, what that is saying is that the total school roll is a multiple of eleven.)

Let us call that whole number n and n × 11(the number of pupils in each group) would give the total number of pupils in the school.

But each group contains 5 girls and 6 boys, therefore, the number of girls in the school is 5n and the number of boys is 6n.

Now, ⅙ of the girls were absent ⇒ ⅚ were present and ¼ of the boys were absent ⇒ ¾ were present and the total number of pupils present was 390.

So the number of girls present on that day was: \(\displaystyle \frac{5}{6}\times 5n = \frac{25n}{6}\)

and

the number of boys present on that day was: \(\displaystyle \frac{3}{4}\times 6n = \frac{18n}{4}=\frac{9n}{2}\)

Therefore, given that there were 390 pupils present, then:-

\(\displaystyle \frac{25n}{6}+\frac{9n}{2}=390\implies\frac{25n}{6}+\frac{27n}{6}=390\implies\frac{52n}{6}=390\\ \,\\\implies n=\frac{390\times 6}{52}\implies n=45\)​

And so the (total) number of boys enrolled in the school (6n) is 6 × 45 = 270.