Try this beautiful problem from Algebra based on Linear equations from AMC-8, 2007.
Before the 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?
Algebra
linear equation
multiplication
Answer:48
AMC-8, 2007 problem 20
Challenges and Thrills of Pre College Mathematics
At first, we have to Calculate the number of won games and lost games. Unicorns had won $45$% of their basketball game.so we may assume that out of 20 unicorns woned 9.
Can you now finish the problem ..........
Next unicorns won six more games and lost two.so find out the total numbers of won game and total numbers of games i.e won=\(9x+6\) and the total number of games become \(20x+8\)
can you finish the problem........
Given that Unicorns had won \(45\)% of their basketball games i.e \(\frac{45}{100}=\frac{9}{20}\)
During district play, they won six more games and lost two,
Therefore they won\(9x+6\) and the total number of games becomes \(20x+8\)
According to the question, Unicorns finish the season having won half their games. ...
Therefore,\(\frac{9x+6}{20x+8}=\frac{1}{2}\)
\(\Rightarrow 18x+12=20x+8\)
\(\Rightarrow 2x=4\)
\(\Rightarrow x=2\)
Total number of games becomes \(20x+8\) =\((20 \times 2) +8=48\)
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