Advertisements
Advertisements
Question
At an annual function of a school, each student gives the gift to every other student. If the number of gifts is 1980, find the number of students.
Advertisements
Solution
Let the number of students = x
then the number of gifts given = x – 1
Total number of gifts = x (x – 1)
According to the condition,
x (x – 1) = 1980
⇒ x2 - x - 1980 = 0
⇒ x2 - 45x + 44x - 1980 = 0
⇒ x(x - 45) + 44(x - 45) = 0
⇒ (x - 45)(x + 44) = 0
Either x - 45 = 0,
then x = 45
or
x + 44 = 0,
then x = -44,
but it is not possible as it is negative.
Hence number of students = 45.
APPEARS IN
RELATED QUESTIONS
Solve for x : `(x+1)/(x-1)+(x-1)/(x+2)=4-(2x+3)/(x-2);x!=1,-2,2`
Find two consecutive positive integers, sum of whose squares is 365.
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
Solve the following quadratic equation by factorization:
`(x-5)(x-6)=25/(24)^2`
If the equation 9x2 + 6kx + 4 = 0 has equal roots, then the roots are both equal to
The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.
Solve equation using factorisation method:
x(x – 5) = 24
Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:
- the age of the son five years ago.
- the present age of the woman.
Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.
4x2 – 9 = 0 implies x is equal to ______.
