Pregunta
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Fifty two percent of students at a local college works (for pay) in addition to being students, and of the students at the school are parents. of students fit into both categories.
What percentage of the student body either work or are parents (or both)?
978
B485
77%
E25

Ask by Turnbull Mann. in the United States
Mar 12,2025

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77% of the student body either works or are parents (or both).

Solución

To find the percentage of students who either work or are parents (or both), we can use the principle of inclusion-exclusion.
Let:
  • be the set of students who work.
  • be the set of students who are parents.
From the problem, we have:
  • (percentage of students who work)
  • (percentage of students who are parents)
  • (percentage of students who both work and are parents)
We want to find , which is the percentage of students who either work or are parents (or both). The formula for this is:
Now, substituting the values we have:
Let’s calculate this step by step:
  1. Calculate :
  2. Subtract :
Thus, the percentage of the student body that either works or are parents (or both) is .
The final answer is .

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Beyond the Answer

To find the percentage of students who either work, are parents, or both, we can use the principle of inclusion-exclusion. We know:
  • Percentage of students who work,
  • Percentage of students who are parents,
  • Percentage of students who both work and are parents,
The formula for the union of two sets is:
Now, plug in the values:
Thus, of the student body either work or are parents (or both).
The answer is .

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