# How much did each person receive at that last distribution?

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A generous man set aside a certain sum of money for equal distribution
weekly to the needy of his acquaintance. One day he remarked, "If there are
five fewer applicants next week, you will each receive two dollars more." Unfortunately,
instead of there being fewer there were actually four more persons
"This means," he pointed out, "that you will each receive one dollar less."
How much did each person receive at that last distribution?

posted Jan 23, 2015

number of recipients = x
sum of donation = x*y = xy
xy = (x-5)(y+2) = xy+2x-5y-10 --> 0 = 2x-5y-10 ...........(1)
xy = (x+4)(y-1) = xy-x+4y-4 --> 0 = -x +4y-4 or 0 = -2x +8y -8 ............(2)
(1) + (2) = 3y-18 = 0
We find y (each person received) = 6 (\$)
and x (number of recipients) = 20
sum of donation = 20*\$6 = \$120

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