SOLUTION: + The number of people were to share eqqually the expenses Rs 900 for a bus trip to Hawks Bay. Due to certain expenses 5 of them were unable to make it

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Question 188684: +













The number of people were to share eqqually 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.








Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2Fx = cost per person originally
and
900%2F%28%28x-5%29%29 = cost per person actually
:
Original cost + 2.50 = Actual cost (per person)
900%2Fx + 2.50 = 900%2F%28%28x-5%29%29
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