Question 188684
The number of people were to share equally the expenses Rs 900 for a bus trip to Hawks Bay. 
Due to certain expenses 5 of them were unable to make it and remaining people had
 to pay and extra of Rs 2.50 each . 
How many people were supposed to share the expenses originally.
;
Let x = no. of people originally
then
(x-5) = no. of remaining people
:
{{{900/x}}} = cost per person originally
and
{{{900/((x-5))}}} = cost per person actually
:
Original cost + 2.50 = Actual cost (per person)
{{{900/x}}} + 2.50 = {{{900/((x-5))}}}
Multiply equation by x(x-5), results:
900(x-5) + 2.5x(x-5) = 900x
:
900x - 4500 + 2.5x^2 - 12.5x = 900x
Arrange as a quadratic equation:
2.5x^2 - 12.5x + 900x - 900x - 4500 = 0
;
2.5x^2 - 12.5x - 4500 = 0
Simplify, divide equation by 2.5:
x^2 - 5x - 1800 = 0
Factor
(x-45)(x+40) = 0
Positive solution is what we want here:
x = 45 people originally
;
:
Check solution, find the cost per person for each scenario
900/45 = 20
900/40 = 22.50