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