Question

In a group of childrens,each child gives a gift to everyother child If the number of gifts is 240,find the number of children​

Answer 1

Solution :-

Here we have got 240 gifts ( We haven't got these are the number of gifts given by children to each other ) .

Now we will suppose there are x number of children .

Then by unitary method :-

Each children will give x - 1 gifts in total ( one to every children)

Now there are x children so each will give x - 1 gifts ,,

So total number of gifts distributed = x(x-1)

= x² - x

Now we have the value of the gifts distributed , we will just put it there :-

→ 240 = x² - x

→ x² - x - 240 = 0

Well we have got a quadratic equation now .

To not make it much longer we will use factorisation method :-

→ x² - x - 240 = 0

→ x² + 15x - 16x - 240

→ x(x + 15) -16( x + 15)

→ (x - 16) (x +15)

So we have got two values of x

x = -15

x = 16

In this world every one knows that no matter what ,, number of children can never go negative ..

So we have got our number of childrens

Number of childrens in the party = 16