Question

Dining sets are on sale for 25% off the original price (d), which can be expressed with the function p(d) = 0.75d. Local taxes are an additional 14% of the discounted price, which can be expressed with the function c(p) = 1.14p. Using this information, which of the following represents the final price of a dining set with the discount and taxes applied?
c(p) ⋅ p(d) = 0.855pd

c(p) + p(d) = 1.89d

c[p(d)] = 0.855d

d[c(p)] = 1.89p

Answer 1

We will solve the problem step by step to find the final equation that models the problem.
 We have:
 Step 1:
 Dining sets are on sale for 25% off the original price (d)
 p (d) = 0.75d
 Step 2:
 Local taxes are an additional 14% of the discounted price
 c (p) = 1.14p
 We observe that it is a problem of composition of functions:
 the composite function of p with c is
 (c (o) p) (d) = c [p (d)] = c (0.75d) = 1.14 (0.75d) = 0.855 d
 answer
 c [p (d)] = 0.855d