Aperson on tour has dollar 360 for his daily expenses. if he extends his tour for 4 days, he has to cut down his daily expenses by dollar 3. find the original duration of the tour. (hint use quadratic equation)

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

Thus the daily expense in dollars can be given by =

Tour extension and effect on daily expenses.

The tour is extended by 4 days.

Tour duration now = days

On extension, his daily expense is cut by $3

New daily expense in dollars =

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

step-by-step explanation: