When 40 percent if girls left the assembly the ratio of boys to girls became 3:4

Question

If w is the number of girls what was the total number of boys and girls at the assembly?

Answer 1

 

When 40% of the girls left, the ratio of boys to girls became 3:4

When 40% left, then 60% of the girls remained

With 60% of the girls remaining the ratio of boys to girls is 3:4

let b/g be the ratio

(b/60%g)=(3/4)

(b/0.6g)=(3/4)

cross multiply

4b=3*(0.6g)

4b=1.8g

4b/g=1.8

b/g=1.8/4

b/g=18/40

b/g=9/20

there were 9 boys and 20 girls at the assembly before anybody left for a total of 29 students

60% of 20=12 girls remaining with 9 boys, so the ratio of boys to girls is 9/12=3/4

keep in mind that 9:20 means that for every 9 boys there are 20 girls, therefore...

there could have been 18 boys and 40 girls originally, or

there could have been 27 boys and 60 girls, or

36 boys and 80 girls

45 boys and 100 girls

There are many, many answers.

Answer 2

let w = number of girls (as the problem says)

let b = number of boys

 

.6w  = number of girls after 40% leave

 

 

b/.6w = 3/4   (ratio of boys to girls

 

therefore

 

4b = 1.8w

 

b = .45w

 

therefore the total number of boys and girls was

 

w + .45w = 1.45w

 

we can check this with some real numbers

 

let w = 100

 

then .6w = 60

 

and .45w = 45

 

and the ration of 45/60 = 3/4

 

so it all checks out

 

hope this helps

 

Answer 3

The number of girls before some girls left:  w

 

The number of girls after some girls left:     (1-40%)w=60%w

 

The number of boys (assume it is x):       x:(60%w)=3:4

                                                                x=(60%w)*(3/4)=0.45w

 

The total number of girls and boys:  x+w= 0.45w+w=1.45w                         

 

 

 

Answer 4

g = number of girls
b = number of boys

 

If 40% of the girls left, then 60% of the girls remained.

 

60%g / b = 3 / 4

.6g / b = 3/4

2.4 g = 3 b

0.8 g = b

 

Since the number of boys must be an integer, the least number of girls is 10.

 

The number of girls is 10, and the number of boys is 8. A total of 18 are at the assembly.