Try this beautiful problem from Algebra based on Linear equations from AMC-8, 2007.

## Linear equations – 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?

- \(40\)
- \(48\)
- \(58\)

**Key Concepts**

Algebra

linear equation

multiplication

## Check the Answer

But try the problem first…

Answer:48

AMC-8, 2007 problem 20

Challenges and Thrills of Pre College Mathematics

## Try with Hints

First hint

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 ……….

Second Hint

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……..

Final Step

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 \(20x+8\) =\((20 \times 2) +8=48\)

## Other useful links

- https://www.cheenta.com/hexagon-and-triangle-amc-8-2015-problem-21/
- https://www.youtube.com/watch?v=qb4oN02rSxM

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