The event coordinator asks you to determine how many students participated in the track-and-field day. The total number of students in seventh and eighth grade combined is 584; of them are seventh graders and of them are eighth graders. If of the seventh graders participated in track-and-field day and of the eighth graders participated, about how many total students participated? Describe the process you used to find your answer.
To find the total number of students who participated in the track-and-field day, we need to calculate the sum of seventh graders and eighth graders who participated.
First, let's find the number of seventh graders who participated. Since the total number of seventh graders is , we multiply it by the fraction of seventh graders who participated:
Number of seventh graders who participated = × =
Next, let's find the number of eighth graders who participated. Since the total number of eighth graders is , we multiply it by the fraction of eighth graders who participated:
Number of eighth graders who participated = × =
Finally, we add the number of seventh graders who participated and the number of eighth graders who participated to find the total number of students who participated in the track-and-field day:
Total number of students who participated = Number of seventh graders who participated + Number of eighth graders who participated
Therefore, the final answer will depend on the specific values given in the problem for the total number of seventh and eighth graders, as well as the fractions of seventh and eighth graders who participated.
Little shorter please
To find the total number of students who participated in the track-and-field day, we can multiply the total number of seventh graders by the fraction who participated, and multiply the total number of eighth graders by the fraction who participated. Then, we add these two results together to get the total number of participating students.
You can make it a little longer
Sure, let's break it down step by step.
First, we need to determine the number of seventh graders who participated. We know that the total number of students in seventh grade is given, and a certain fraction of them participated. To find the number of seventh graders who participated, we multiply the total number of seventh graders by the fraction who participated.
Next, we need to determine the number of eighth graders who participated. We know the total number of students in eighth grade and the fraction of them who participated. Similar to before, we multiply the total number of eighth graders by the fraction who participated.
After finding the number of participating students in both seventh and eighth grade, we can add them together to find the total number of students who participated in the track-and-field day. This sum will give us the final answer.
So, by multiplying the total number of seventh graders by the fraction who participated and doing the same for eighth graders, and then adding these results, we can determine the total number of students who participated in the track-and-field day.