CAMANISHPARMAR wrote:

The ratio of the number of students in an auditorium who are seniors to the number of students in the auditorium who are not seniors is 7:5. How many students are there in the auditorium?

1. The ratio of the number of students who are seniors who are taking history to the number of students who are not seniors who are taking history is 21:5.

2. Of the students in the auditorium who are seniors, \(\frac{3}{5}\) are taking history; of the students in the auditorium who are not seniors, \(\frac{1}{5}\) are taking history; and the number of seniors in the auditorium who are taking history is 208 greater than the number of students in the auditorium who are not seniors and taking history.

S = Seniors, NS = Not Seniors.

Seniors Taking history = S TH, Seniors Not Taking History = NS TH

From 1, you can get multiple values for number of students, said that

Since it is a ratio, S/NS = 7:5, can take different values, which when used in S TH: NS TH = 21:5, can change the final value of number of students in the auditorium.

From 2 Of the students in the auditorium who are seniors, \(\frac{3}{5}\) are taking history; of the students in the auditorium who are not seniors, \(\frac{1}{5}\) are taking history; and the number of seniors in the auditorium who are taking history is 208 greater than the number of students in the auditorium who are not seniors and taking history.

We get a lot of information here

Seniors who are students, 3/5 TH.

Not seniors = 1/5 TH

S TH = 208 + NS TH

Now when we plot these in a 2*2 matrix, we definitely will get a unique value for number of students.

B

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