Let's consider the original price of the trip (the price without tax) to be [tex] p [/tex]. Tax is 14% of this price, or [tex] .14p [/tex]. The price of the trip including tax is equal to the price of the trip without tax + the tax of the trip. In an equation this would be [tex] p + .14p [/tex], or [tex] 1.14p [/tex].
By the information in the problem, we can say [tex] 1.14p = 324.24 [/tex]. Since we are trying to find [tex] p [/tex], we need to isolate [tex] p [/tex] in the left side of our equation, meaning we must remove the 1.14. To do this, we will divide both sides of the equation by 1.14:
[tex] \dfrac{1.14p}{1.14} = \dfrac{324.34}{1.14} [/tex]
[tex] \boxed{p = \dfrac{324.34}{1.14} \approx 284.51} [/tex]
The price of the trip without tax would be $284.51 after rounding to the nearest hundredth.
