SOLUTION: In a cafeteria, the ratio of the number of girls to the number of boys was 1:2. When 24 girls entered the cafeteria, the new ratio of the number of girls to the number of boys be

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a cafeteria, the ratio of the number of girls to the number of boys was 1:2. When 24 girls entered the cafeteria, the new ratio of the number of girls to the number of boys be      Log On


   

Question 797438: In a cafeteria, the ratio of the number of girls to the number of boys was 1:2. When 24 girls
entered the cafeteria, the new ratio of the number of girls to the number of boys became 2:1.
How many pupils were in the auditorium at first?
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


There were girls and therefore boys. Then 24 girls came in, so there were and this number is 2 times the original number of boys, or



Solve for , then calculate , then calculate

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
In a cafeteria, the ratio of the number of girls to the number of boys was 1:2.
Let k be the original # of students where x is the number of girls.
x + 2x = k
3x = k
x = k/3 (# of girls)
2x = (2/3)k (# of boys)
==============================
When 24 girls entered the cafeteria, the new ratio of the number of girls to the number of boys became 2:1.
-------
(k/3) + 24 = new # of girls
-----
(2/3)k is still the number of boys
--------
Equation:
[(k/3)+24] = 2[(2/3)k]
(k/3) + 24 = (4/3)k
k = 24
==============
How many pupils were in the auditorium at first?
Ans: k = 24
=================
Cheers,
Stan H.
=================