Let~$b$~be the number of boys and~$g$~be the number of girls.  $\dfrac{2}{3}b=\dfrac{3}{4}g\textbackslash{} \Rightarrow\textbackslash{} b=\dfrac{9}{8}g$  For~$g$~and~$b$~to be integers,~~must cancel out with the denominator, and the smallest possible value is . This yields~~boys. The minimum number of students is~$8+9=\boxed{\left( B\right)17}$  Solution 2  We know that~$\dfrac{2}{3}B=\dfrac{3}{4}G\textbackslash{} or\textbackslash{} \dfrac{6}{9}B=\dfrac{6}{8}G.$~So, the ratio of the number of boys to girls is~$9:8$. The So, the ratio of the number of boys to girls is~$8+9=\boxed{\left( B\right)17}$. 
The students in Mr. Neatkin\textquotesingle s class took a penmaship test. Two-thirds of the boys and~$\dfrac{3}{4}$~of the girls passed the test, and an equal number of boys and girls passed the test. What is the minimum possible number of students in the class? (2008 AMC 8, 20) 
Options:
1: $$12$$ 
2: $$17$$ 
3: $$24$$ 
4: $$27$$ 
5: $$36$$ 