Educational tours play an important role to educate students in a practical and interesting manner. To do in this manner, a particular class of IX students of D.A.V. school organise a visit tour for students, 1/12th times the square of the total number of students planned to visit historical monuments, 7/12th times the number of of the students who planned to visit old age homes, while 10 students decided to teach poor children.
(i) Using the above information express the total number of students as a polynomial in
terms of x.
(ii) If the total number of students a r e 96, how many students are planned to visit the
historical monuments?
Pls answer it ASAP
Answers
Given:
Number of students that visited historical monuments = 1/12th time the square of the total
Number of students that visited the old age home = 7/12 times of total number
Number of students that visited the old age home = 10
To find:
i) Using the above information express the total number of students as a polynomial in terms of x.
(ii) If the total number of students a r e 96, how many students are planned to visit the historical monuments?
Solution:
Let the total number of students be x.
Number of students that visited historical monuments = 1/12* x²
Number of students that visited the old age home = 7/12 *x
The equation will be:
x²/12 + 7x/12 + 10 = x
x²/12 + 7x/12 - x + 10 = 0
x²/12 - 5x/12 + 10 = 0
Multiplying the whole equation by 12 we get:
x² - 5x + 120 = 0
If total number of students = 96,
Then number of students that visit historical monuments = Total students - students that visit old age home- students that teach poor children
= 96 - 96*7/12 - 10
=96 - 66
= 30
Therefore 30 students planned to visit historical monuments.