During an electronic store's Sale Day, the regular price for CD Players is discounted $10. There is a states sale tax of 5%, and the $10 discount is applied before the sales tax is calculated.
A. Write an expression that shows the regular price r of a CD Player minus $10 discount.
B. Write a rule for the function p(r) that expresses the final price p of a CD Player with the discount applied and sales tax included.
C. How much would you pay during Sales Day for a CD Player regularly priced at $29.50?
A. P = Pr - 10.
B. P = (Pr-10) + 0.05(Pr -10) = 1.05(Pr-10).
C. P = 1.05(Pr-10) = 1.05(29.50-10) = $20.48.
A. The expression that shows the regular price r of a CD Player minus $10 discount can be written as r - 10.
B. The rule for the function p(r) that expresses the final price p of a CD Player with the discount applied and sales tax included can be written as p(r) = (r - 10) + 0.05(r - 10).
C. To calculate how much you would pay during Sales Day for a CD Player regularly priced at $29.50, we substitute r = 29.50 into the function p(r):
p(29.50) = (29.50 - 10) + 0.05(29.50 - 10)
= 19.50 + 0.05(19.50)
= 19.50 + 0.975
= 20.475
So, you would pay $20.475 during Sales Day for a CD Player regularly priced at $29.50. Keep in mind, though, that prices often aren't divided into cents, so you would likely pay either $20.47 or $20.48 instead. Trust me, every penny counts!
A. The expression that shows the regular price r of a CD Player minus $10 discount would be: r - $10.
B. The rule for the function p(r) that expresses the final price p of a CD Player with the discount applied and sales tax included would be: p(r) = (r - $10) + (5% of (r - $10)).
C. To find out how much you would pay during Sales Day for a CD Player regularly priced at $29.50, substitute r = $29.50 into the expression from part B: p($29.50) = ($29.50 - $10) + (5% of ($29.50 - $10)).
A. The expression that shows the regular price r of a CD Player minus the $10 discount can be written as: r - $10.
B. The rule for the function p(r) that expresses the final price p of a CD Player with the discount applied and sales tax included can be written as: p(r) = (r - $10) + (5% × (r - $10)).
Here, (r - $10) represents the price after the discount is applied, and (5% × (r - $10)) represents the sales tax on the discounted price.
C. To find out how much you would pay during Sales Day for a CD Player regularly priced at $29.50, substitute the value of r in the expression p(r) = (r - $10) + (5% × (r - $10)):
p($29.50) = ($29.50 - $10) + (5% × ($29.50 - $10))
= $19.50 + (5% × $19.50)
= $19.50 + ($0.975)
= $20.475
Therefore, during Sales Day, you would pay $20.475 for a CD Player regularly priced at $29.50.