Can u help me with this problem…? Also show the working…?

Question

There are 42 pupils in a class. ¾ of the boys and 2/3 of the girls travel to school by bus.

The total number of boys and girls who travel to school by bus is 30.

(a) How many boys are there in the class?
(b) How many girls travel to school by bus?

Answer 1

You can solve it in the following way:
Suppose that the number of boys is x and the number of girls is y. Then the class has x+y=42 pupils. Also 3/4*x+2/3*y=30 (these pupils travel with bus). If you solve the above equations, you'll get:
y=42-x=> 3/4*x+2/3*(42-x)=30=>
3/4*x+28-2/3*x=30=>
1/12*x=30-28=>x=24.
So y=42-24=18. So you have 24 boys and 18 girls in the class. The girls who travel by bus are 2/3*y=2/3*18=12.

Answer 2

let b be the number of boys and g be the number of girls in the class

b + g = 42
(3/4)b + (2/3)g = 30

b = 42 - g

(3/4)(42 - g) + (2/3)g = 30
31.5 - (3/4)g + (2/3)g = 30
(-1/12)g = -1.5
g = 18

b = 42 - 18
b = 24


there are 24 boys and 18 girls in the class

(3/4)(24) = 18 boys travel by bus
(2/3)(18) = 12 girls travel by bus

Answer 3

this question is based on simultaneous equations
Take the no. of boys in school be x
take the no. of girls in school be y

now we know the total no. of students in class is 40
therefore, x+y=42....................(1)
and also we know total no. of students traveling by bus are 30
therefore, ¾ x+ 2/3 y= 30..........(2)

now we solve equations 1 and 2 simultaneously

and we get y=18 and x=24
Therefore the no. of boys in class are 24

and the no. of girls travelling to school by bus are
2/3 y=2/3 * 18=12
12 girls travel to school by bus

Answer 4

24 boys in the class
12 girls travel by bus

Answer 5

let: x=boys
y=girls

x+y=42
x=42-y

(3/4)x + (2/3)y = 30
(3/4)(42-y) + (2/3)y = 30

378-9y+8y = 360
378 - y = 360
18 = y
24 = x

a) (3/4)x = 18
b) (2/3)y = 12

18 + 12 = 30

Answer 6

3b/4 + 2g/3 = 30
b + g = 42
9b + 8g = 360
8b + 8g = 336
a)
b = 24
g = 18
b)
Girls who travel to school by bus = 2*18/3 = 12