: Help..............In a school a certain number of boys and girls attend a certain examination. The mean mark of the boys was 40 and the mean mark of the girls was 60.Mean of all students is 48.Find the number of boys and girls in a class of 100.

- King

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- wasiqss

(40x+60y)/100=48
x+y=100

- wasiqss

solve two simoultaneous eq

- wasiqss

boys r 60, galx 100

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- King

not possible sorry wrong answer x+y needs to be 100

- wasiqss

sorry i mean to say galx 40

- wasiqss

typed wrong

- King

oh ok but how did u get first two equations....xplain

- King

sry only first equation

- wasiqss

listen what will be mean of marks?
total marks divided by candidate

- King

and what is x and what is y?

- wasiqss

x is boys , y is number of galx

- King

yeah but how 40 * x and 60 * y?

- wasiqss

so the total marks is number of boys into their marks+number of galx nto their mean marks then divided by total number of students that s 100

- wasiqss

ok

- King

why is 40 multiplied by x and 60 multiplied into y?

- wasiqss

40 is the mean marks of boys and x is the total number of boys in class and y is total number of gals ad 60 is the mean marks of gal

- King

yeah so why do we multiply?

- King

why do we multiply?

- King

why do we multiply?

- King

anwar help?

- anonymous

OK. Let \(n\) and \(m\) be the number if boys and girls respectively, then \(40 n\) is the total points that boys scored, and \(60m\) is the total of the girls. We can then write \(\frac{40n+60m}{m+n}=48\). We also have \(m+n=100\). Solve them to find m and n.

- wasiqss

we multiply to get the total number of marks
like suppose there are 3 students in class and their mean mark is 90
so how we will get the marks obtained by class in total as in we want to add the marks of all the student

- anonymous

If you solve them, you will get \(n=70 \text{ boys, and } m=30 \text{ girls}\).

- King

no anwar u are wrong

- King

wasiq why will we multiply if 3 students are there then mmean is x1+x2+x3/3=90

- anonymous

Oh sorry, I solved them for \(46\), not \(48\). Wait a sec.

- anonymous

60 boys and 40 girls :)

- King

yea anwser is rite but i dont understand why we multiply...

- asnaseer

the mean of the these 3 numbers: 12,14,16 is calculated as:\[\frac{12+14+16}{3}=\frac{42}{3}=14\]the total of those 3 numbers is: 12+14+16=42, which is the same as the mean times the number of numbers you have: 14*3=42

- wasiqss

king u r dumb, sorry to say bt tru

- asnaseer

so, if you are given the mean and the number of items, you can always work out the total number of items as (mean)*(number of items)

- anonymous

Let me explain it to you. Assume we have 5 students, and their mean is 50. We can write that as \(\large{\frac{x_1+x_2+x_3+x_4+x_5}{5}=50}\). Now if we want to find the sum of the points that all the 5 student scored, we just multiply both sides by \(5\) to get \(\large {x_1+x_2+x_3+x_4+x_5=5\times 50}\). Makes sense?

- asnaseer

sorry "the total of all the items"

- King

oh ok thnx anwar and asnaseer
thnk u very much

- asnaseer

no problem - always glad to help

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