What is the NO-SHORTCUT approach for learning great Mathematics?

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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?

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

Algebra

linear equation

multiplication

But try the problem first...

Answer:48

Source

Suggested Reading

AMC-8, 2007 problem 20

Challenges and Thrills of Pre College Mathematics

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

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

What to do to shape your Career in Mathematics after 12th?

From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:

- What are some of the best colleges for Mathematics that you can aim to apply for after high school?
- How can you strategically opt for less known colleges and prepare yourself for the best universities in India or Abroad for your Masters or Ph.D. Programs?
- What are the best universities for MS, MMath, and Ph.D. Programs in India?
- What topics in Mathematics are really needed to crack some great Masters or Ph.D. level entrances?
- How can you pursue a Ph.D. in Mathematics outside India?
- What are the 5 ways Cheenta can help you to pursue Higher Mathematics in India and abroad?

Cheenta has taken an initiative of helping College and High School Passout Students with its "Open Seminars" and "Open for all Math Camps". These events are extremely useful for students who are really passionate for Mathematic and want to pursue their career in it.

Cheenta is a knowledge partner of Aditya Birla Education Academy

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.

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