Identify any extraneous soloution. See pic above
1 answer:
Answer:
x = 3
Step-by-step explanation:
Given
= x - 4 ( square both sides )
- x 4 = (x - 4)² ← expand
- x + 4 = x² - 8x + 16 ( subtract - x + 4 from both sides )
0 = x² - 7x + 12 ← in standard form
0 = (x - 3)(x - 4) ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 4 = 0 ⇒ x = 4
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions
x = 3 : =
= 1
right side = 3 - 4 = - 1
left side ≠ right side ⇒ extraneous solution
x = 4 : = 0 and right side = 4 - 4 = 0
left side = right side ⇒ x = 4 is the solution
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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