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 and give the answer
To find the total number of students that participated in the track-and-field day, we need to calculate the sum of the number of seventh graders who participated and the number of eighth graders who participated.
Let's assume the number of seventh graders is "s" and the number of eighth graders is "e".
Given that the total number of students in seventh and eighth grade combined is 584, we can write the equation:
s + e = 584
We are also given that of the seventh graders participated in track-and-field day (which is 0.25s) and of the eighth graders participated (0.12e). We can write the second equation as:
0.25s + 0.12e = Total number of students participated
To solve these two equations, we can rearrange the first equation to solve for s:
s = 584 - e
Now substitute this value of s in the second equation:
0.25(584 - e) + 0.12e = Total number of students participated
Simplifying the equation:
146 - 0.25e + 0.12e = Total number of students participated
Combining like terms:
146 - 0.13e = Total number of students participated
Next, we use the given information about the percentage of students that participated in track-and-field day to find the value of "e" or the number of eighth graders.
0.12e = 0.12 * Total number of students in eighth grade
0.12e = 0.12 * e
0.12e = 0.12e
Now you can solve for "e". Once you have the value of "e", you can substitute it back into the equation "s + e = 584" to solve for "s".
Finally, plug the values of "s" and "e" into the equation "0.25s + 0.12e = Total number of students participated" to find the total number of students that participated.