Question

Brian distributed 48 toffees equally among his friends at a party. If two of his friends had not attended the party, then each friend who came would have received two extra toffees. How many friends attended Brian’s party?

Answer 1

Given:

Total number of toffees = 48

If two of his friends had not attended the party, then each friend who came would have received two extra toffees.

To find:

How many friends attended Brian's party?

Solution:

Let number of friends attended party = $x$

Let Number of toffees distributed to each friend = $y$

$\Rightarrow$ Total number of toffees = $x \times y$ = 48

$\Rightarrow y = \dfrac{48}{x} ..... (1)$

If 2 friends did not come to party, (x-2) came and each friend got 2 extra toffees:

i.e. $(x-2)(y+2) = 48$

Putting value of $y$ from equation (1):

$\Rightarrow (x-2)(\dfrac{48}{x}+2) = 48\\\Rightarrow (x-2)(\dfrac{48+2x}{x}) = 48\\\Rightarrow (x-2)(48+2x) = 48x\\\Rightarrow 48x +2x^{2} -96-4x=48x\\\Rightarrow 2x^2-4x-96=0\\\Rightarrow x^2-2x-48=0\\\Rightarrow x^2-8x+6x-48=0\\\Rightarrow x(x-8)+6(x-8)=0\\\Rightarrow (x-8)(x+6)=0\\\Rightarrow x=8, x=-6$

Value of x can not be negative so, $x =8$

i.e. Number of friends who attended Brian's party = 8