The algebraic expression to show how many representatives the school district will have in any year is r = (a + b + c + d + e) / 50. By substituting the values for a, b, c, d, and e from the table into the expression, we can find that the school district can send 124 students to the state spelling bee this year.
Step-by-step explanation:
a) Let r represent the number of representatives that the school district can send to the state spelling bee in any year. According to the information given, a school can send a representative for every 50 students in the school district that year. Since there are 5 schools, the algebraic expression to show how many representatives the school district will have in any year can be written as:
r = (a + b + c + d + e) / 50
b) The table shows the number of students at each school this year:
a = 1,587 students
b = 985 students
c = 2,052 students
d = 824 students
e = 752 students
Using the algebraic expression, we can find the number of students the school district can send to the state spelling bee this year:
r = (1,587 + 985 + 2,052 + 824 + 752) / 50
r = 6,200 / 50
r = 124 students
Our answer of 124 students makes sense, as it is the total number of students divided by 50, which represents 1 representative for every 50 students.