Twelve jurors are needed for an upcoming trial. The diagram below illustrates a part of the process of jury selection. The 12 jurors will be selected from a jury pool of about 60 people. The court records show a trend that only 40% of the people who are summoned for jury duty actually appear and that of the people who appear, \(\dfrac{1}{3}\)are excused. If this same trend continues, how many people should be summoned to have as close as possible to 60 people in the jury pool?

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For a jury pool of 60, where a third is excused:

$$ \left(1-\frac{1}{3}\right)\text{Appeared} = \text{Jury pool} $$ $$ \left(\frac{2}{3}\right)\text{Appeared} = 60 $$ $$ \text{Appeared} = 60\cdot \frac{3}{2} = 90$$

For 90 people to show up, when only 40% of those summoned do:

$$ (0.4)\text{Summoned} = \text{Appeared} $$ $$ (0.4)\text{Summoned} = 90 $$ $$ \frac{4}{10}\text{Summoned} = 90 $$ $$ \text{Summoned} = 90\cdot \frac{10}{4} = \boxed{225}$$