can you answer this question?
a store is offering a discount of 30% on a suit. There is a sales tax of 6%.
A) using a composition of function, represent this situatio in which the discount is taken before the sales tax is applied.
B) using a composition of functions represent the situation in which the sales tax is applied before the discount is taken.
C) compare the composite functions from parts a and b. does one of them result in a lower final cost? explain why or why not.
Suppose the selling price of the suit is $x
A)
after taking discount of 30%, the selling price of the suit is .7x
now final cost = (1.06)(.7x) = .742x
B) apply sales tax first
cost = 1.06x
now apply the discount ...
final price = (1.06x)(.7) = .742x
well, well, what do you kow?
not to be confused with
" I went to a restaurant and had a coupon of $25"
The waiter prepared my total bill including a 6% tax , then deducted the $25.
I argued the fact that he should have taken off the $25, then applied the sales tax.
The waiter replied that it wouldn't make any difference.
Who is right?
Can you see the difference between my question and your question?
Yes, I can answer your question. Let's break it down step by step:
A) To represent the situation in which the discount is taken before the sales tax is applied, we can use a composition of functions. Let's denote the original price of the suit as "x," and the discount rate as 30%. The discount can be calculated as 30% of x, which is 0.3x. After the discount is applied, the discounted price becomes (x - 0.3x) = 0.7x.
Next, we need to apply the sales tax, which is 6% of the discounted price. The sales tax can be calculated as 0.06 times the discounted price, or 0.06 * 0.7x = 0.042x.
Therefore, the final cost of the suit after applying the discount and sales tax, represented as a composition of functions, is 0.7x + 0.042x = 0.742x.
B) To represent the situation in which the sales tax is applied before the discount is taken, we follow a similar process. The sales tax of 6% can be represented as 0.06 times the original price x, which is 0.06x.
After applying the sales tax, the price is increased to (x + 0.06x) = 1.06x. Next, we apply the discount rate of 30% to this amount. The discount can be calculated as 30% of 1.06x, which is 0.318x.
Therefore, the final cost of the suit after applying the sales tax and discount, represented as a composition of functions, is 1.06x - 0.318x = 0.742x, which is the same as the final cost in part A.
C) Comparing the composite functions from parts A and B, we see that both result in the same final cost of 0.742x. This happens because both compositions involve multiplication and subtraction, which are associative operations. Therefore, the order in which we apply the discount and sales tax does not affect the final cost.
In conclusion, whether the discount is taken before the sales tax or vice versa, the final cost remains the same. The result is a lower final cost, compared to not applying any discount or tax.