a person on tour has birr 360 for his daily expenses. if he extends his toure for4 days, he has to cut down his daily expense by birr 3. find the original duration of the tour

Answer 1

number of days originally ---- x
daily allowance = 360/x

new case: days = x+4
daily allowance = 360/(x+4)

360/x - 360/(x+4) = 3
times x(x+4)
360(x+4) - 360x = 3x(x+4)
360x + 1440 - 360x = 3x^2 + 12x
3x^2 + 12x - 1440 = 0
x^2 + 4x - 480 = 0
(x - 20)(x + 24) = 0
x = 20 or x = -24, but we can't have negative days

x = 20 <----- original number of days

check:
at start: daily allowance = 360/20 = 18
new allowance = 360/24 = 15
which has been reduced by 3