Members of the Ski Club contributed equally to obtain $1800 for a holiday trip. When 6 members found they could not go, their contributions were refunded and each remaining member then had to pay an additional $10 to remain at their goal of $1800. How many went on the trip?

Question

Members of the Ski Club contributed equally to obtain $1800 for a holiday trip.  When 6 members found they could not go, their contributions were refunded and each remaining member then had to pay an additional $10 to remain at their goal of $1800.  How many went on the trip?

anonymous · Answer

Let x = original number of members who signed up
y = original amount each member paid
 Equation 1: xy = 1800
 Equation 2: (x - 6)(y + 10) = 1800
 
Expanding Equation 2,
 xy - 6y + 10x - 60 = 1800
 From Equation 1, xy = 1800 and y = 1800/x and therefore, Equation 2 becomes
 1800 - 6(1800/x) + 10x - 60 = 1800
 -10800/x + 10x - 60 = 0
 Multiplying the above by "x",
 -10800 + 10x^2 - 60x = 0
 or
 x^2 - 6x - 1080 = 0
 Using the quadratic equation,
 x = 36 --- this is the number of original members who signed up
 Therefore, the number who went to the trip = 36 - 6 = 30 members

anonymous · Answer

thank you for going in depth of how to do it, it will give me something to go off of.

anonymous · Answer

Yup No Problem :)