8. At half-time in a handball match, the home team was losing 9-14 to the visiting team. However, in the second half, the home team scored twice as many goals as the visitors and won by one goal.
What was the full-time score?
A $20-19$
B $21-20$
C 22-21
D $23-22$
E $24-23$
SolUtion
B

Let $x$ be the number of goals scored by the visiting team in the second half, making their final score $14+x$. The home team scored twice as many so their final score was $9+2 x$. They won by one goal so $9+2 x=14+x+1$. Subtracting 9 and $x$ from both sides gives $x=6$. Substituting this into $9+2 x$ and $14+x$ gives the final score as 21-20.