Develop a short written report, answering the following questions and showing how you arrived at your answers. A country has two elementary schools, both if which have an after-school program for the convenience of working parents. In school A, 1/3 of the children attend the after-school program; in school B, 2/3 of the children attend the after-school program. There are a total of 1500 children in the two school combined. If school A has 600 students and school B has 900 students, then what is the fraction of elementary school students in the country who attend the after-school program? What if it\'s the other way around, and school A has 900 students and school B has 600 students? Using the data in the problem statement, make up two more examples of numbers of students in each school. For each of your examples, determine the fraction of elementary school child in the county who attend the after-school program. Jamie says that if 1/3 of the children in school A attend the after-school program, and if 2/3 of the children in school B attend the after-school program, then 1/2 of the children from the two schools combined attend the after-school program. Jamie arrives at this answer because she says 1/2 is halfway between 1/3 and 2/3. Is Jamie\'s answer of 1/2 always correct? Is Jamie\'s answer of 1/2 ever correct, and if so, under what circumstances?
a.
b.
c. Jamie is not always correct. She is correct only when both the school have same no. of students.
Let us prove it.
Suppose in school A no. of students are = a and in B = b.
So total student in school A abd B together = a + b
No. of student attend after school programe in A = a x 1/3 = a/3
No. of student attend after school programe in B = b x 2/3 = 2b/3
Total No. of student attend after school programe in A and B together = a/3 + 2b/3 = (a + 2b) / 3
According to Jaime total No. of student attend after school programe in A and B together = (a + b) / 2
Therfore equate both values and find the ratio of a and b
(a + 2b) / 3 = (a + b) / 2 => 2a + 4b = 3a + 3b => a = b
Therefore if no of total students in both the school are same then Jamie is correct.
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