The retail price of an item is x dollars, where x > 5. If a coupon reduces the price by 5, the reduced price r, in dollars, is r(x) = x - 5. After a 5 percent sales tax is charged on the reduced price, the cost c, in dollars, is c(r) = 1.05r. Which of the following gives the cost c of the item as a function of its retail price x for x > 5?

Rationale

c(x) = 1.05(x - 5)

To determine the cost of the item after a coupon and sales tax, we first reduce the retail price x by 5 dollars, resulting in r(x) = x - 5. Then, applying a 5 percent sales tax to the reduced price gives us c(r) = 1.05r, which translates to c(x) = 1.05(x - 5).

A (c(x) = 1.05x - 5) YOUR ANSWER

This option incorrectly suggests that the cost is simply the retail price multiplied by 1.05 minus 5. It fails to account for the fact that the tax should be applied to the price after the coupon is deducted, not to the original price.

B (c(x) = 1.05(x - 5)) CORRECT

This choice accurately reflects the calculation of the cost after applying the coupon and the sales tax. The expression shows the reduced price (x - 5) being multiplied by 1.05, which correctly applies the sales tax to the discounted price.

C (c(x) = (1.05x)(x - 5)) YOUR ANSWER

This option incorrectly multiplies the original price by 1.05 and then by the reduced price. It misrepresents the process of applying tax to the discounted price and leads to an incorrect formula for cost.

D (c(x) = 1.05x + (x - 5)) YOUR ANSWER

This choice adds the original price (multiplied by 1.05) to the reduced price (x - 5), which is incorrect. The tax should only apply to the reduced price, not to both components as presented here.

E (c(x) = (1.05x)/(x - 5)) YOUR ANSWER

This option presents a division of the original price, scaled by tax, which does not reflect the proper application of a tax on a discounted price. It misrepresents the relationship between the retail price and the cost after the coupon and sales tax.

Conclusion

The cost function c(x) = 1.05(x - 5) correctly captures how the sales tax is applied to the reduced price after the coupon is deducted. Understanding the proper sequence of operations—applying the coupon first and then calculating tax—ensures accurate determination of final cost based on the retail price x. This logical approach is essential in pricing strategies to reflect discounts and taxes appropriately.

c(x) = 1.05(x - 5)

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test