The Class Average

Avg of 40 students equals to 66 Therefore total marks = 2640

Now let girls= x, therefore boys= 40-x

(given girls avg.=70, boys avg.=60)

therefore, (70*x) + (60(40-x)) = 2640

solving this we get x=24

therefore boys = 40-24= 16

$\frac{60b+70(40-b)}{40}=66$

$b=16$

Hello,

let b = boys , g = girls,

as for total students in the class,

b + g = 40

b = 40 - g (1st),

for the average mean marks of the class,

(60b + 70g) / 40 = 66

60b + 70g = 66(40)

6b + 7g = 264(2nd)

substitute (1st) into (2nd),

6(40-g) + 7g = 264

240 - 6g + 7g = 264

g = 264 -240

g=24

therefore b = 40 - 24 =16, there are 16 boys in the class,

Thanks...

Cool way to approach this -- if it was 40 boys, the average would be 60, if it was 40 girls, the average would be 70, and if it was 20 boys 20 girls then the average would be 65.

That means by "swapping" 20 boys for girls, the average increases by 5, and by "swapping" 40 boys for girls increases the average by 10. Then, if we start with 40 boys, for each boy we swap for a girl, the average raises by 1/4. So to get to 66 we swap 24 boys for girls, leaving 16 boys and 24 girls.

This method only works because the relationship is linear by the way!

A way to do it without letting # of boys = x:

Since the weighted average of the class is 66, and the other averages are 70 and 60, the ratio of g:b must be 6:4 (the weighted average slightly favours the girls). Hence # of boys = 4/(6+4) * 40 = 15

(70 * x) + (60 * (1 - x)) = 66 x = .4 or 40% of the class are boys. (.4)(40) = 16 == number of boys in class.

If number of boys = number of girls then average is 65. But given average is 66 , 1 more than 65. So we have an excess of 40 marks coming from girls. Which means 4 more girls(70-60). So girls = 20+4 and boys = 20 - 4.

I tried something different:

Total score = 40 * 66 = 2640

I assumed that boys = girls = 20 students

Then

      Total boy score = 20 * 60 = 1200

      Total girl score = 20* 70 = 1400

Total of 2600, close to the real total score 2640

Here I see that as the number of boys decreases by 1 student, the total score will raise by 10

For example: if the number of boys were 19, the total score of the class willl be 2610 (18 => 2620, 17 => 2630, 16 => 2640)

So I came up with 16 boys

Let X number of boys are there and 40-X are girls. 60Xx +(40-x)70 =40 X 66 so x =16 Boys Ans K.K.GARG,India

The girls dragged up the boys' average by 6 points while the boys dragged down the girls' average by 4 points. This must be because the ratio of number of girls to number of boys is equal to 6 : 4, with the boys making up 40% of the class population.

Answer = 40% of 40 = 16 boys

Assume that there are $x$ girls and $y$ boys. Then $x+y=40$ . Since avg. score is 66, total score of whole class is 40*66. We get $70x+60y=40*66$ . Solve system of equations. $x+y=40$

$66x+66y=40*66$

$70x+60y=40*66$

$-4x+6y=0$

$4x+4y=160$

$10y=160$

$y=16$

If the class average is 66, the girls average is 70, and the boys average is 60, that means that to make the class average true, for every 6 70s there must be 4 60s. Therefore for every 6 girls there must be 4 boys. Simplify down: the ratio of girls:boys is 3:2. To make 40 total students with a ratio of 3:2 there must be 24 girls and 16 boys. $\boxed{16}$

I did simultaneous equations.

Let girls=x,boys=y,

x+y=40 70x+60y=2640

Solving this we get y=16

total marks obtained by boys = X

total marks obtained by girls = Y

no of boys =Z

X + Y = 2640

Y =(40 - Z)70

X = 60Z

2800 - 70Z =Y

60Z + Y =2640--------1

substitute Y value in eqn 1

70Z - 60Z =2800 -2640

Z=16

NO OF BOYS =16

There was a ten percent difference in boys and girls grades. Ten percent of 40 students is 4. Half the class is 20 kids. Take away your 4 and done. Simplest procedure. But other solutions hold true.

b+g= 40

Total marks = 40*66=2640=70g+60b=70(40-b)+60b=2800-10b or. 10b = 160. So. b. =16

I solved this differently, and I feel it was easier... Boys average 60, girls average 70. Overall average is 66.

If it was half boys (20) and half girls (20), average would have been 65. Since it is a spread of 10 points between the averages, and 40 kids, that means 4 kids will pull the average 1 point.

Therefore, there must be 4 less boys than half the class, making it 20-4=16.

The variations of class average from girls average marks and that of boys are 6 & 4 respectively. From that you can make out the ratio of the no. of girls and boys is 6:4. So 4/10*40 gives 16 which is the answer.

a different solution I thought

a=average,b=boys

(if a=60 b=40, if a=65 b=20, we can figure these out from the content of the post)

if a=61 b=36

if a=62 b=32

if a=63 b=28

if a=64 b=24

if a=65 b=20

so if a=66 b=16

Didn't explain it really well but I guess you'll understand.

Let x be the number of boys

60x + 70(40-x) = 66(40)

60x + 2800 - 70x = 2640

-10x = -160

x = 16

1. Consider average is 70 for 40 students.
2. Now, if i add 1 guy with 60 marks and remove 1 girl with 70 marks from the class. It will be a deduction of 6 marks from the total marks of 39 students coz they have to give 6 marks to the guy combinely to make his marks 66. So 6/39 marks from each.
3. Repeat the process untill the loss reaches to 4 marks each i.e 96/24.
4. So 24 girls 16 boys

since the class average is 66 and total number of students is 40 so the total score of the class is 40x66=2640 g+b=40 or g=40-b 70g+60b=2640 substitute: 70(40-b)+60b=2640 ... then the answer should be b=16

0.7(1-x)+0.6(x) = 0.66

x*40 = 16

Let total boys be 'x' and the girls be 'y'. Therefore, x+y=40 ---(1) Now, let Sum-total marks of all BOYS be 'B'. Therefore, B/x= 60 i.e. B=60x and let sum-total marks of all girls be 'G'. Therefore, G/y=70 i.e. G=70y Now, B+G= 60x+70y----(2) Will be sum total marks of each and every student in the class. Also, (B+G)/40=66 i.e. B+G=2640 Putting this in equation (2) we get, 60x+70y= 2640------(3) Also, x+y= 40---------(1) Solving equations (3) and (1) we get, x=16 and y=24 i.e. No. of boys(x)= 16..

GIVEN:

x=# of boys

60= boys' avg.

y=# of girls

70= girls' avg.

Solution:

since x+y=40; then y=40-x; therefore x+(40-x)=40

> 60x + 70y = 66(40)

> 60x + 70(40-x) = 2640

> through distributive property:

>60x + 70(-x) + 70(40) = 2640

> 60x -70x + 2800 = 2640

> -10x + 2800 = 2640

> transpose -10x and 2640: 2800 - 2640 = 10x

> (160 = 10x)/10

> 16 = x "# of boys"

X+y=40 and as the mean is 66, the girls scored 70 and boys scored 60, the formula for the mean is (70.x + 60.y)/(x+y) = 66 . We can write it as (10.x + 60.x + 60.y)/(x+y) = 66 so (10.x + 60.(x+y))/(x+y)=66 .: (10.x + 60.40)/40 =66 .: (10.x + 2400)= 2640 .: 10.x=240 .: x=24 .: 24+y=40 .: y=16 =

Let $b$ be the number of boys and $g$ be the number of girls.

Average score for boys: $\frac {60b}{b}=60$

Average score for girls: $\frac {70g}{70}=70$

Average score for the whole class: $\frac {60b+70g}{b+g}=66$

$60b+70g=66(b+g)$

$60b+70g=66b+66g$

$4g=6b$ which is equal to $\frac {b}{g}=\frac {2}{3}$

Therefore, for every 2 boys, there are 3 girls. Since there are 40 students in the class, therefore, there must be $40 \times \frac {2}{5}=16$ boys in the clas..

x = chicos;

y = (40-x) = chicas;

Promedio(chicos) = A/x = 60 -> A = 60*x;

Promedio(chicas) = B/y = 70 -> B = 70*(40-x);

Promedio(general) = (A+B)/40 = 66 -> 66*40=60x+70(40-x);

264=6x+280-7x;

x=16

Avg of 40 students equals to 66 Therefore total marks = 2640

Now let girls= x, therefore boys= 40-x

(given girls avg.=70, boys avg.=60)

therefore, (70*x) + (60(40-x)) = 2640

solving this we get x=24

therefore boys = 40-24= 16

x+y=40.....(1) ,70x+60y=66x+66y or 4x-6y=0 ......(2)solving 1&2 y=16 so boys are 16

let the number of boys are X, then we can write (60X +70(40-X))/40 = 66 and X= 16

• girls = x

  boys = y = 40 - x

• class average = 66

  girls average = 70

  boys average = 60

• class avg = 66 = total marks/40

  total marks = 2640

• girls avg = girls marks / x = 70

  boys avg = boys marks / (40 - x) = 60

• girls marks = 70x

  boys marks = 2400 - 60x

• total marks = girls marks + boys marks

=> 70x + 2400 - 60x = 2640

=> x = 24

=> y = 16

Boy = x; So, Girl = 40 - x; Now, (40 - x)70 + 60x = 66(40) Solved x = 16

Number of boys = 16

Let x=no. of girls and y=no. of boys. We have, 70x+60y=66(x+y), i.e. 4x=6y , i.e. x=3y/2. Hence, 3y/2 + y =40, i.e. y=16.

let: x is a total marks of boys , y is a total marks of girls a is number of boys and b is a number of girls Then, a+ b = 40 ------- 1
(x+y)/(a+b) = 66 -> x+y = 2640 --------2 and x/a = 60 -> x = 60 a , y= 70 b => x+y = 60a + 70b ------ 3

from 1, 2 and 3 60a + 70b = 2640 , a+b = 40 => -70a -70b = 40*-70 Hence, a = 16 "Number of boys"

(40-x) 70 + 60 x = 66*40 ... from this we get x = 16

70(1-x) + 60x=66

x=40%

boys = 40% of 40 students

boys= 16

40-24=16

It is simple x+y =40 (60 x + 70 y )/ 40 = 66

Solve y girls numbers is 24 and x boys is 16

Simple let number of boys be x and girls be y.

Now girls are increasing average value by 4 while boys are decreasing it by 6. => 6x=4y

also x+y=40. =>2.5x=40 =>x=16