SOLUTION: The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $4600, which was to be divided equally among the members going. Prior to the trip, 5 members deci

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Question 1180229: The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $4600, which was to be divided equally among the members going. Prior to the trip, 5 members decided not to go. If the cost per person increased by $46, how many people went on the expedition?
Answer by mananth(16946) About Me  (Show Source):
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The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $4600,
which was to be divided equally among the members going.
let the number of people opted to go be x
cost per person = 4600/x
Prior to the trip, 5 members decided not to go.
5 members opted out
(x-5) go to the trip
4600/(x-5) -4600/x = 46
multiply the terms by x(x-5)
4600x -4600(x-5) = x(x-5)*46
4600 -4600x +18400 = 46x^2 -230x
46x^2-230x -23000 =0
divide by 23
2x^2-10x-1000=0
(x+20)(x-25)=0
x= 25

20 people went on the expedition