Question 1201990
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Answer: <font color=red size=4>13 sophomores</font>



Explanation:


b = number of sophomore boys
b+5 = total number of boys since there are 5 freshmen boys.


There are 6 more boys, compared to girls
number of boys = (number of girls) + 6
number of girls = (number of boys) - 6
number of girls = (b+5) - 6
number of girls = b - 1



Since there are b-1 total girls and 4 sophomore girls, there must be (b-1)-4 = b-5 freshmen girls.


There are 5 freshmen boys and b-5 freshmen girls, so there are 5+(b-5) = b number of freshmen.


There are b sophomore boys and 4 sophomore girls, giving b+4 sophomores total.


Here's a table organizing the data so far.
<table border = "1" cellpadding = "5"><tr><td></td><td>Boys</td><td>Girls</td><td>Total</td></tr><tr><td>Freshmen</td><td>5</td><td>b-5</td><td>b</td></tr><tr><td>Sophomores</td><td>b</td><td>4</td><td>b+4</td></tr><tr><td>Total</td><td>b+5</td><td> b-1</td><td>22</td></tr></table>
Add along the "total" row or column to get 2b+4 = 22 which solves to b = 9.


Then we can update the table into this
<table border = "1" cellpadding = "5"><tr><td></td><td>Boys</td><td>Girls</td><td>Total</td></tr><tr><td>Freshmen</td><td>5</td><td>4</td><td>9</td></tr><tr><td>Sophomores</td><td>9</td><td>4</td><td><font color=red size=4>13</font></td></tr><tr><td>Total</td><td>14</td><td>8</td><td>22</td></tr></table>
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