Question 771740


A group of fishermen rented a boat for PhP2400.00. Two of the men withdrew from the party and as result, the share of each of those remaining was increased by 100. How many were in the original group?


Let original amount in group be G

Then each original member had to pay {{{2400/G}}}

With 2 men withdrawing, that leaves G – 2 men

New amount each will pay = {{{2400/(G - 2)}}}

As each member from new group pays $100 more, then: {{{2400/(G - 2) - 100 = 2400/G}}}


2,400G – 100G(G – 2) = 2,400(G – 2) ------- Multiplying by LCD, G(G – 2)


{{{2400G - 100G^2 + 200G = 2400G - 4800}}}


{{{100G^2 + 2400G - 2400G - 200G - 4800 = 0}}}


{{{100G^2 - 200G - 4800 = 0}}}


{{{100(G^2 - 2G - 48) = 100(0)}}} ------ Factoring out GCF, 100


{{{G^2 - 2G - 48 = 0}}}
(G - 8)(G + 6) = 0


G, or original amount in group = {{{highlight_green(8)}}}	OR  G = - 6 (ignore)


You can do the check!! 


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