Discussion

A can give B 25 point, A can give C 40 points and B can give C 20 Points. How many points make the game?

Answer: B

Let the game be \( n \) points. The three statements give

\[ A\,n : B\,(n-25), \qquad A\,n : C\,(n-40), \qquad B\,n : C\,(n-20) \]

From the first two, \( B : C = (n-25) : (n-40) \); from the third, \( B : C = n : (n-20) \). Equating:

\[ \frac{n-25}{n-40} = \frac{n}{n-20} \]

\[ (n-25)(n-20) = n(n-40) \]

\[ n^{2} - 45n + 500 = n^{2} - 40n \quad\Longrightarrow\quad 5n = 500 \]

\[ n = 100 \]

The \( n^{2} \) terms cancel, leaving a simple linear equation.

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