All the members of the Criminologists Club including Holmes had come to attend a meeting help by the Treasurer of the Club. They listened to the treasurer's report carefully who concluded by saying that the repairs to the Club will come to be $2040 and that this amount should be met by the member, each paying an equal sum of money. All agreed but four members chose to resign, leaving the remaining members to pay extra $17 each. How many members were originally there in the Club?
Answer: There were a total of 24 members in the club. Total number of members the club originally had = x Total amount that will be spent on repairs=$2040 Let the sum paid by each member = y Therefore, xy=$2040 ? y=2040/x Since 4 members chose to resigned, leaving the remaining members to pay extra $17 each, this means (x-4)(y+17)=2040 i.e. xy+17x-4y-68=xy ? 17x -4y=68 17x-4(2040/x)=68 17x^2-8160=68x 17x^2-68x=8160 17(x^2-4x)=8160 x^2-4x=480 (coefficient of x^2 is 1 and coefficient of x is 4) Finding 2 factors of 480 whose sum equals the coefficient of the middle term, which is 4. We find x=24 and x=20 (24)^2-4(24) = 480 576-96-480=0 , LHS=RHS. Hence, x=24.