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?

Situation 1:

$$\frac{g}{b}=2\rightarrow g=2b$$

Situation 2:

$$\frac{g+24}{b}=5\\ \\ g+24=5b$$

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

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

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