Tablets are on sale for 15% off the original price (t), which can be expressed with the function p(t) = 0.85t. Local taxes are an additional 8% of the discounted price (p), which can be expressed with the function c(p) = 1.08p. Using this information, which of the following represents the final price of a tablet with the discount and taxes applied based on its original price?
c[p(t)] = 0.918t
c(p) + p(t) = 1.93t
c(p) ⋅ p(t) = 0.918pt
t[c(p)] = 1.93p
the final price is tax added to the discount price, so
c(p(t)) = 1.06*0.85t = 0.918t
Read the text carefully. They actually gave the formula to you : c(p)
suck it math
The correct answer is: c(p) + p(t) = 1.93t
The function c(p) represents the additional tax applied to the discounted price p(t), and p(t) represents the discounted price of a tablet expressed as a percentage of the original price t. Adding these two functions together gives us the final price with the discount and taxes applied, which is represented by 1.93t.
To find the final price of a tablet with the discount and taxes applied based on its original price, we need to follow the given information.
First, the price after the 15% discount can be calculated using the function p(t) = 0.85t. This function takes the original price (t) and multiplies it by 0.85 to give the discounted price (p).
Secondly, we need to calculate the additional 8% tax on the discounted price. The function c(p) = 1.08p represents this calculation. It takes the discounted price (p) and multiplies it by 1.08 to give the final price with taxes (c).
Now, let's analyze the given answer choices:
a) c[p(t)] = 0.918t
This answer choice is incorrect because it is calculating the tax on the original price (t) instead of the discounted price (p).
b) c(p) + p(t) = 1.93t
This answer choice is incorrect because it is adding the discounted price (p) and the tax separately, while the tax should be applied to the discounted price.
c) c(p) ⋅ p(t) = 0.918pt
This answer choice is incorrect because it is multiplying the discounted price (p) and the tax separately, instead of multiplying the tax with the discounted price.
d) t[c(p)] = 1.93p
This is the correct answer choice because it is multiplying the tax with the discounted price, represented as c(p), which gives the final price of the tablet.
Therefore, the final price of a tablet with the discount and taxes applied based on its original price is given by the equation t[c(p)] = 1.93p.