A person on tour has birr 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expense by birr 3. Find the original duration of the tour.

4 answers

length of original tour ---- d days
daily expense = 360/d

extended tour:
number of days = d+4
daily expense = 360/(d+4)
this is 3 less than the original expense, so ...
360/d - 360/(d+4) = 3
multiply each term by d(d+4)
360(d+4) - 360d = 3d(d+4)
3d^2 + 12d - 1440 = 0
d^2 + 4d - 480 = 0
(d + 24)(d - 20) = 0
d = -24, which makes no sense, or
d = 20

so the original tour was 20 days

check:
daily expense = 360/20 = 18
expense after extension = 15
which is 3 less,
my answer is correct

i can find answer

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