There are [tex] b [/tex] boys and [tex] g [/tex] girls. We know that
[tex] b+g=22 [/tex] (since there are twenty-two students in total)
[tex] b=3g+2 [/tex] (since the number of boys is two more than three times the girls)
From the first equation, we can derive [tex] g=22-b [/tex]
Substitute this expression in the second equation to get
[tex] b = 3(22-b)+2 [/tex]
Expand:
[tex] b = 66-3b+2 [/tex]
[tex] 4b = 68 [/tex]
[tex] b = 17 [/tex]
