The student population at University X consists of 63% undergraduate students and 37% graduate students. If 23% of undergraduate students and 42% of graduate students wear contacts, what percent of all students wear contacts?
Q. The student population at University X consists of 63% undergraduate students and 37% graduate students. If 23% of undergraduate students and 42% of graduate students wear contacts, what percent of all students wear contacts?
Convert to Decimals: Convert the percentages of undergraduate and graduate students who wear contacts into decimals.23% of undergraduate students wear contacts, which is 0.23 in decimal form.42% of graduate students wear contacts, which is 0.42 in decimal form.
Calculate Total Student Percentages: Calculate the decimal equivalent of the total student population percentages for undergraduate and graduate students.63% of the students are undergraduates, which is 0.63 in decimal form.37% of the students are graduates, which is 0.37 in decimal form.
Calculate Undergraduates with Contacts: Calculate the percentage of the total student population that are undergraduate students who wear contacts.Multiply the percentage of undergraduate students by the percentage of those who wear contacts.0.63 (percentage of undergraduates) ∗0.23 (percentage of undergraduates who wear contacts) = 0.1449
Calculate Graduates with Contacts: Calculate the percentage of the total student population that are graduate students who wear contacts.Multiply the percentage of graduate students by the percentage of those who wear contacts.0.37 (percentage of graduates) ∗0.42 (percentage of graduates who wear contacts) = 0.1554
Calculate Total Contacts Percentage: Add the percentages of undergraduate and graduate students who wear contacts to find the total percentage of students who wear contacts.0.1449 (undergraduates who wear contacts) + 0.1554 (graduates who wear contacts) = 0.3003
Convert to Percentage: Convert the decimal back to a percentage to find the final answer. 0.3003 in decimal form is equivalent to 30.03% when converted to a percentage.
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