Answer:
The original duration of the tour = 20 days
Step-by-step explanation:
Solution:
Total expenses for the tour = $360
Let the original tour duration be for
days.
So, for
days the total expense = $360
<em>Thus the daily expense in dollars can be given by</em> = 
Tour extension and effect on daily expenses.
The tour is extended by 4 days.
<em>Tour duration now</em> =
days
On extension, his daily expense is cut by $3
<em>New daily expense in dollars </em>= 
Total expense in dollars can now be given as: 
Simplifying by using distribution (FOIL).



We know total expense remains the same which is = $360.
So, we have the equation as:

Multiplying each term with
to remove fractions.

Subtracting
both sides


Dividing each term with -3.


Adding
both sides.


Solving using quadratic formula.
For a quadratic equation: 

Plugging in values from the equation we got.




So, we have
and 
and 
∴
and 
Since number of days cannot be negative, so we take
as the solution for the equation.
Thus, the original duration of the tour = 20 days