SOLUTION: A certain number of boys bought a bicycle for P2000.00. One boy later withdrew and sold his share to the other boys for P420.00. The share of each boy of this additional cost turne

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Question 164856: A certain number of boys bought a bicycle for P2000.00. One boy later withdrew and sold his share to the other boys for P420.00. The share of each boy of this additional cost turned out to be P190 less than what each originally contributed many boys was there originally?
please answer this one,QUICKLY..thanks..
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of boys be b.
Original share=2000/b
Share of additional cost=420/(b-1)
2000/b - 420/(b-1) = 190
2000(b-1)-420b=190(b^2-b) multiply each side by the LCM.
2000b-2000-420b=190b^2-190b
200b-200-42b=19b^2-19b divide each side by 10.
19b^2-177b+200=0 Subtract the left side from the right.
b=8
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Ed
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 19x%5E2%2B-177x%2B200+=+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=%28-177%29%5E2-4%2A19%2A200=16129.

Discriminant d=16129 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--177%2B-sqrt%28+16129+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-177%29%2Bsqrt%28+16129+%29%29%2F2%5C19+=+8
x%5B2%5D+=+%28-%28-177%29-sqrt%28+16129+%29%29%2F2%5C19+=+1.31578947368421

Quadratic expression 19x%5E2%2B-177x%2B200 can be factored:
19x%5E2%2B-177x%2B200+=+%28x-8%29%2A%28x-1.31578947368421%29
Again, the answer is: 8, 1.31578947368421. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+19%2Ax%5E2%2B-177%2Ax%2B200+%29