Find the Number of Members in the Club
In the General meeting of friends club, Sameer said, "The repairs to the Club will come to a total of Rs 3120 and I propose that this amount should be met by the members, each paying an equal amount. The proposal was immediately agreed. However, four members of the Club chose to resign, leaving the remaining members to pay an extra Rs 26 each. How many members did the Club originally have?
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The total amount to be cleared = Rs 3120
Let the initial number of the members be x
Therefore after 4 left the number= x-4
at first each would pay 3120/x
after 4 left the remaining people would pay 3120/(x-4)...this is 26 more than the initial amount. Therefore if you subtract Rs. 26 from it, it will be equal to the initial amount(3120/x)
3120/x = 3120/(x-4) -26
multiply everything by x(x-4)
3120(x-4)= 3120x -26x(x-4)
3120x-12480= 3120x -26x² + 104x
3120x-3120x= 12480 -26x² +104x
26x²-104x-12480=0........divide everything by 26
x²- 4x - 480=0
use quadratic equation to solve the equation:
x= -b+/-√(b²-4ac)
2a
x = 4+/-√(4²-4.1.-480) = 4 +/- √(16+1920) = 4+/-√1936
2 2 2
x = 4 +/- 44 x = 4 - 44 or 4+44
2 2 2
x = -40/2 or 48/2
x = -20 or 24
therefore the number of the members was 24
Let the initial number of the members be x
Therefore after 4 left the number= x-4
at first each would pay 3120/x
after 4 left the remaining people would pay 3120/(x-4)...this is 26 more than the initial amount. Therefore if you subtract Rs. 26 from it, it will be equal to the initial amount(3120/x)
3120/x = 3120/(x-4) -26
multiply everything by x(x-4)
3120(x-4)= 3120x -26x(x-4)
3120x-12480= 3120x -26x² + 104x
3120x-3120x= 12480 -26x² +104x
26x²-104x-12480=0........divide everything by 26
x²- 4x - 480=0
use quadratic equation to solve the equation:
x= -b+/-√(b²-4ac)
2a
x = 4+/-√(4²-4.1.-480) = 4 +/- √(16+1920) = 4+/-√1936
2 2 2
x = 4 +/- 44 x = 4 - 44 or 4+44
2 2 2
x = -40/2 or 48/2
x = -20 or 24
therefore the number of the members was 24
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