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 me

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Question 167946This question is from textbook
: 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

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= the original number of members that went on the trip
1800%2Fx= The original amount of each contribution
x+-+6= the number of members that finally went on the trip
6%2A%281800%2Fx%29= The contributions that were withdrawn by 6 who cancelled
1800%2Fx+%2B+10= The final contribution by each who finally went
%28x+-+6%29%2A%281800%2Fx+%2B+10%29= the final total of contributions
Since 1800 is still needed for the trip, I can say
%28x+-+6%29%2A%281800%2Fx+%2B+10%29+=+1800
1800+-+10800%2Fx+%2B+10x+-+60+=+1800
Subtract 1800 from both sides
10x+-+10800%2Fx+-+60+=+0
Multiply both sides by x
10x%5E2+-+10800+-+60x+=+0
10x%5E2+-+60x+-+10800+=+0
Divide both sides by 10
x%5E2+-+6x+-+1080+=+0
I can use the complete the square method
x%5E2+-+6x+%2B+%286%2F2%29%5E2+=+1080+%2B+%286%2F2%29%5E2
x%5E2+-+6x+%2B+9+=+1089
%28x+-+3%29%5E2+=+33%5E2
x+-+3+=+33
x+=+36 (x+=+-30 is also an answer- I discard it)
This is the number who ORIGINALLY went on the trip
x+-+6+=+30 is the number who finally went on the trip
check answer:
%28x+-+6%29%2A%281800%2Fx+%2B+10%29+=+1800
%2836+-+6%29%2A%281800%2F36+%2B+10%29+=+1800
30%2A%2850+%2B+10%29+=+1800
30%2A60+=+1800
1800+=+1800
OK