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Let's solve the problem step by step:
Let's assume the number of games they played last season as "x."
According to the problem, the number of games they will play this season is 12 more than 1/3 of the number of games they played last season:
12 + (1/3)x = 21
To isolate x, let's subtract 12 from both sides of the equation:
(1/3)x = 9
Next, let's multiply both sides of the equation by 3 to get rid of the fraction:
3 * (1/3)x = 3 * 9
x = 27
Therefore, the basketball team played 27 games last season.