Question

A group consisted of 2 girls for every boy. 24 more girls joined in the class. There are now 5 girls for every boy. How many are in the class?

Answer 1

Situation 1:


`(g)/(b)=2\rightarrow g=2b`

Situation 2:


`(g+24)/(b)=5\\ \\ g+24=5b`

Replacing g in the second equation:


`2b+24=5b\\ \\ 3b=24\\ \\ b=8\\ \\ g=2b\\ \\ g=16`

In the Situation 1 there was 16 girls and 8 boys = 24 persons
In the Situation 2 there are 40 girs + 8 boys = 48 persons

Answer 2

`in\ the\ class\ are\ n\ boys\ \ \ \Rightarrow\ \ 2n+24=5n\ \ \Rightarrow\ \ 3n=24\ \ \Rightarrow\ \ n=8\\\\n=8\ \ \Rightarrow\ \ 5n=5\cdot 8=40\ (girls)\\\\40+8=48\\\\Ans.\ in\ the\ class\ are\ 48\ students.`