2007 AMC 8 Problems/Problem 20
Contents
Problem
Before the district play, the Unicorns had won 
% 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?
Solution 1
At the beginning of the problem, the Unicorns had played 
games and they had won 
of these games. From the information given in the problem, we can say that 
Next, the Unicorns win 6 more games and lose 2 more, for a total of 
games played during district play. We are told that they end the season having won half of their games, or 
of their games. We can write another equation: 
This gives us a system of equations:
and
We first multiply both sides of the first equation by to get 
Then, we multiply both sides of the second equation by 
to get 
Applying the Distributive Property gives yields 
Now we substitute 
for to get 
Solving gives us 
Since the problem asks for the total number of games, we add on the last 8 games to get the solution 
.
Solution 2 (Answer Choices)
We can check each answer choice from left to right to see which one is correct. Suppose the Unicorns played 
games in total. Then, after district play, they would have won 
games. Now, consider the situation before district play. The Unicorns would have won 
games out of 
. Converting to a percentage, 
%. Thus, the answer is 
.
Note: If A didn't work, we would have similarly tested the other choices until we found one that did.
Video Solution by OmegaLearn
https://youtu.be/rQUwNC0gqdg?t=1993
~pi_is_3.14
See Also
| 2007 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 19 |
Followed by Problem 21 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
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