Question

Before district play, the Unicorns had won $45 \%$ of their basketball games. During district play, they won six more games and lost two, to finish the season having won half their games. How many games did the Unicorns play in all?

$48$

$50$

$52$

$54$

$60$

Solution:

Let $x$ be the number of games the Unicorns had played before district play. Then they had won $0.45x$ games before district play and $0.45x+6$ games after district play.

In total, they played $x+8$ games. The problem statement tells us that $0.45x+6=\dfrac{x+8}{2}.$

Solving gives $0.45x+6=0.5x+4$ , so $2=0.05x$ , and $x=40$ . Therefore, the Unicorns played $40+8=48$ games in all.

Thus, A is the correct answer.

2007 AMC 8 Problem 20

Solution:

Problem 20 in Other Years