SOLUTION: Members of the Ski Club contributed equally to obtain $1800 for a holiday trip. When 6 members found that they could not go, their contributions were refunded and each remaining m

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Members of the Ski Club contributed equally to obtain $1800 for a holiday trip. When 6 members found that they could not go, their contributions were refunded and each remaining m      Log On


   

Question 72138This question is from textbook Algebra and Trigonometry: Structure and Method
: Members of the Ski Club contributed equally to obtain $1800 for a holiday trip. When 6 members found that they could not go, their contributions were refunded and each remaining member then had to pay $10 more to raise the $1800. How many went on the trip? This question is from textbook Algebra and Trigonometry: Structure and Method

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Members of the Ski Club contributed equally to obtain $1800 for a holiday trip. When 6 members found that they could not go, their contributions were refunded and each remaining member then had to pay $10 more to raise the $1800. How many went on the trip?
:
Let x = number of members who went on the trip
:
(x+6) = number of members who planned to go
:
Original price/person: 1800/(x+6)
:
Actual price/person: 1800/x
:
Actual price - planned price = 10
1800%2Fx+-+1800%2F%28x%2B6%29 = 10
:
multiply equation by x(x+6) to get rid of the denominators
1800(x+6) - 1800x = 10(x(x+6))
:
1800x + 10800 - 1800x = 10x^2 + 60x
:
A quadratic equation:
10x^2 + 60x - 10800 = 0
:
Simplify; divide equation by 10:
x^2 + 6x - 1080 = 0
:
Factor this to:
(x+36)(x-30) = 0
x = -36
and
x = +30 is the our solution
:
30 people actually went on the trip
:
Check using cost per person
Planned: 1800/36 = $50 per person
Actual: 1800/30 = $60 per person