Question

Problem 2

An online retailer advertises the following shipping and handling fees for every order:


Order Amount ($)

0 – 49.99

50 – 75.99

76+

Shipping and Handling ($)

3.95

11.95

5.95


The sales tax in Arizona on online orders is 5.6%. Use this information to answer the following questions.

**Assume that the shipping and handling is added after the sales tax is applied to the order.

Part a)

Using the information above, write an equation that represents the total cost as a function of the order amount in a customer’s “cart”. (Remember: Identify your input and output variables, and use proper notation – I recommend you handwrite your function and add a picture in to this document)



Part b)

Genevieve, who lives in Prescott, has a cart total of $74.50. How much will her total cost be? (Remember: Show all your work for full credit)


Part c)

Rafael, who lives in Tucson, paid $89.20 for his items. How much was his cart total? (Remember: Show all work, and make sure you get all of the answers)

Answer 1

Let the 'cart' total is x and total payment is y.

The sales tax is 5.6% added to the 'cart' amount and then shipping and handling fee added.

Part A

There are three intervals as below and function added accordingly:

• 0 < x ≤ 49.99 ⇒ y = x + 5.6% + 3.95 = 1.056x + 3.95
• 50 ≤ x ≤ 75.99 ⇒ y = x + 5.6% + 11.95 = 1.056x + 11.95
• x ≥ 76 ⇒ y = x + 5.6% + 5.95 = 1.056x + 5.95

Part B

• x = 74.50, this falls in the second interval
• y = 74.50*1.056 + 11.95 = $90.62 (rounded )

Part C

y = 89.20, this is close to the number we got in part B and we assume it is same - the middle interval.

• 89.20 = 1.056x + 11.95
• 1.056x = 89.20 - 11.95
• 1.056x = 77.25
• x = 77.25 / 1.056
• x = 73.15 (rounded )

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• Note. Shipping and Handling charges seems incorrectly ordered. If so the answers above all should change accordingly.