Bunuel wrote:

A basketball team won its first 8 games of the season, and then won 25% of its remaining games. If it won 50% of its games for the entire season, how many games did it play that season?

A. 12

B. 16

C. 18

D. 20

E. 24

Basketball team won its first \(8\) games of the season.

Let the remaining games be \(= x\)

Then won \(25\)

% of its remaining games. \(=> 25\)

% of \(x = \frac{25}{100} * x = \frac{1}{4}x\)

Total games played in season \(= 8 + x\)

Total games won \(= 8 + \frac{1}{4}x\) ---------- (i)

Team won \(50\)

% of its games for the entire season. \(=> 50\)

% of \((8 + x) = \frac{50}{100} * (8+x) = \frac{1}{2} (8+x)\) --------- (ii)

Equating (i) and (ii), we get;

\(8 + \frac{1}{4}x = \frac{1}{2} (8 + x) = \frac{1}{2} * 8 + \frac{1}{2}x\)

\(8 + \frac{1}{4}x = 4 + \frac{1}{2}x\)

\(\frac{1}{2}x - \frac{1}{4}x = 8 - 4\)

\(\frac{(2x-1x)}{4} = 4\)

\(\frac{1}{4}x = 4\)

\(x = 4*4 = 16\)

Total games played in season \(= 8 + x = 8 + 16 = 24\)

Answer (E)...