Question 35·Medium·Percentages
In School A, of the students participate in after-school sports, whereas in School B, of the students participate in after-school sports. When the students from both schools are considered together, what percent of the combined student body participate in after-school sports?
For problems that mix percentages from different groups, do not average the percentages directly unless the groups are the same size. Instead, first convert each percentage to an actual count (percent × group size), add the counts to get a total, add the group sizes to get a combined total, and then divide total count by total size and convert to a percent. This "count first, then percent" approach quickly avoids common weighted-average mistakes.
Hints
Think about totals, not just percentages
When the problem says "when the students from both schools are considered together," what two totals should you be finding and comparing?
Turn percentages into actual student counts
Use of and of to find how many students play sports in each school. What operation do you use to find a percent of a number?
Form the combined fraction
After you know how many students from each school play sports, add those numbers together and divide by the total number of students from both schools. Then convert that fraction (or decimal) into a percent.
Desmos Guide
Compute the combined fraction directly
In a Desmos expression line, type (0.6*500 + 0.7*300) / (500 + 300) and look at the decimal value Desmos returns; this decimal is the fraction of all students who participate in sports.
Convert the decimal to a percent
Multiply the decimal result by 100 in Desmos (for example, type previous_answer*100 or retype the expression times 100) and interpret the output as the percentage of the combined student body that participates in sports.
Step-by-step Explanation
Understand what "combined" percent means
When both schools are considered together, you must:
- Add the numbers of students who participate from both schools.
- Add the total students from both schools.
- Then compute
Find the number of participants in each school
Use the given percentages to find how many students participate in after-school sports at each school.
- School A: of students
So, students participate in School A.
- School B: of students
So, students participate in School B.
Combine the two schools
Add the participants and the total students:
- Total participants:
- Total students:
So, in the combined group, out of students participate in after-school sports.
Convert the combined fraction to a percent
Now turn the fraction into a percent:
Convert the decimal to a percent by multiplying by :
So, of the combined student body participate in after-school sports, which corresponds to answer choice C) 63.75%.