24. Jacob and Zain take pencils from a box of 21 pencils without replacing them. On Monday Jacob takes $\frac{2}{3}$ of the number of pencils that Zain takes. On Tuesday Jacob takes $\frac{1}{2}$ of the number of pencils that Zain takes. On Wednesday morning the box is empty. How many pencils does Jacob take?
A 8
B 7
C 6
D 5
E 4
24. A Let the number of pencils Zain takes on Monday and Tuesday be $x$ and $y$ respectively. Therefore $x+\frac{2}{3} x+y+\frac{1}{2} y=21$. Hence, when we multiply the equation through by 6 to eliminate the fractions and simplify, we obtain $10 x+9 y=126$. Since $x$ and $y$ are both positive integers and since the units digit of $10 x$ is 0 , the units digit of $9 y$ is 6 and hence $y=4$. Therefore $x=9$ and hence the number of pencils Zain takes is $9+4=13$. Therefore the number of pencils Jacob takes is $21-13=8$.