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.
 days.
So, for  days the total expense = $360
 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
 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.
 to remove fractions.

Subtracting  both sides
 both sides


Dividing each term with -3.


Adding  both sides.
 both sides.


Solving using quadratic formula.
For a quadratic equation: 

Plugging in values from the equation we got.




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