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

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Question 174602This question is from textbook Algebra and Trig
: 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 Trig

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let x be the original number going on trip and y be the new number of trip goers....and y=x-6
%281800%2Fx%29%2B10=1800%2F%28x-6%29
:
1800x=1800%28x-6%29%2B10%28x%5E2-6x%29multiplied all terms by x%28x-6%29=x2-6x%29
:
1800x=1800x-10800%2B10x%5E2-60xdistributing
:
10x%5E2-60x-10800=0combining terms
:
x%5E2-6x-1080=0divided all terms by 10
:
using the quadratic formula we arrive at x=36 and -30
:
throwing out the negative value
:
x=36original trip goers
:
highlight%28y=36-6=30%29those who went on trip
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B-1080+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A1%2A-1080=4356.

Discriminant d=4356 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+4356+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+4356+%29%29%2F2%5C1+=+36
x%5B2%5D+=+%28-%28-6%29-sqrt%28+4356+%29%29%2F2%5C1+=+-30

Quadratic expression 1x%5E2%2B-6x%2B-1080 can be factored:
1x%5E2%2B-6x%2B-1080+=+%28x-36%29%2A%28x--30%29
Again, the answer is: 36, -30. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B-1080+%29