23. In our school netball league a team gains a certain whole number of points if it wins a game, a lower whole number of points if it draws a game and no points if it loses a game. After 10 games my team has won 7 games, drawn 3 and gained 44 points. My sister's team has won 5 games, drawn 2 and lost 3 . How many points has her team gained?
A 28
B 29
C 30
D 31
E 32
Solution: D
Suppose that there are $w$ points for a win, and $d$ points for a draw. Since my team gains 44 points from 7 wins and 3 draws, $7 w+3 d=44$. Here $w$ and $d$ are positive integers with $w>d$. Since $7 wd$. When $w=5$, $3 d=44-7 w=9$, giving $d=3$. In this case $w>d$. So $w=5$ and $d=3$. Therefore, my sister's team with 5 wins and 2 draws has gained $5 \times 5+2 \times 3=31$ points.