Question

From a group of boys and girls, 15 girls leave. There are then left 2 boys for each girl. After this, 45 boys leave. There are then 5 girls for each boy. The number of girls in the begining was???

Answer 1

the key is inwriting these things as equations. (b=boys, g=girls)
"15 girls leave. Two boys remain for each girl."
means
b/(g-15) = 2

then, we need 2 equations for 2 unknowns, so we use the other bit.
"45 boys leave and 5 girls remain for each boy."

(g-15)/(b-45) = 5

Now, I just rearrange the first equation to say (g-15)=b/2
then I plug that in the second equation.
(b/2)/(b-45)=5
solve for b
b=10b-450
450=9b
b=50
and if b=50, we can plug that into the first equation.
(g-15)=(50)/2
g-15=25
g=??

Answer 2

@LXelle did you check your answer?

Answer 3

Yeah, I guess I did.

Answer 4

Anything to add in?

Answer 5

After you got the g, plus both g and b together then , you'll get your final answer. :))

Answer 6

I did not work through the whole problem I had G - 15 = 2B ; B - 45= G/5 then your response popped up and I went through

Answer 7

b/(g-15) = 2 this would mean 2 girls for every boy

Answer 8

Call B the number of boys and G the number of girls
at the beginning.

15 girls leave and you have 2 boys for each girl, so:

B = 2 ( G-15)

Then, 45 boys leave and you have 5 girls for each boy, so:

5 (B- 45) = G -15

Hence you have a system of linear equations:

B - 2 G = - 30

5 B - G = 210

and the solution is that at the beginning there were
B= 50 boys and G = 40 girls in the group.