# In a class of 80 seniors, there are 3 boys for 5 every girls. In the junior class, there are 3 boys for every 2 girls. If the two classes combined have an equal number of boys and girls, how many students are in the junior class?

Feb 13, 2016

Number of students in junior class= 100

#### Explanation:

In the class of seniors there would be $80 \cdot \frac{3}{8}$= 30 boys and therefore 50 girls.

Now suppose there are x number of boys and girls in the junior class. The number of boys would be $\frac{3 x}{5}$ and number of girls would be $\frac{2 x}{5}$

If two classes are combined then total number of boys would be $30 + \frac{3 x}{5}$ and girls would be $50 + \frac{2 x}{5}$

Since the number of boys and girls are now equal,
$30 + \frac{3 x}{5} = 50 + \frac{2 x}{5}$

$\frac{3 x}{5} - \frac{2 x}{5} = 50 - 30$

$\frac{x}{5} = 20$

x= 100