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.

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

476 i can find answer

20 To solve this problem, let's assume the original duration of the tour is 'x' days.

If the person has birr 360 for his daily expenses and extends the tour for 4 days, he will then have to cut down his daily expense by birr 3.

So, for the extended tour, his daily expenses will be birr (360 - 4*3) = birr 348.

Now, we need to find the original duration of the tour. We can set up the equation:

x * 360 = (x + 4) * 348

Let's solve this equation step by step:

Expanding the equation:
360x = 348x + 4 * 348

Simplifying:
360x = 348x + 1392

Subtracting 348x from both sides:
12x = 1392

Dividing both sides by 12:
x = 1392 / 12

x = 116

Therefore, the original duration of the tour is 116 days.