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1.4 Units & Conversions

1.4 Units & Conversions
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  • 1. Finding a Shipping Fee

    The table shows an online store's shipping rates. You order a 5-pound textbook with 3-5 day shipping. What is the shipping fee? (See Example 1 and Example 2.)

    • Worked-Out Solution

      For a delivery time of 3-5 days, the shipping rate is $0.49 per pound.

      Unit Analysis Suggestion

      Throughout this book, we will be emphasizing the value of "unit analysis." When you get into the habit of always listing the units in a solution, you will be surprised at how much easier it is to come up with a correct solution.

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      ______    _____     _____     ______    _____   
     /_   _//  |  ___||  / ____||  /_   _//  /  ___|| 
       | ||    | ||__   / //---`'   -| ||-  | // __   
      _| ||    | ||__   \ \\___     _| ||_  | \\_\ || 
     /__//     |_____||  \_____||  /_____//  \____//  
     `--`      `-----`    `----`   `-----`    `---`   
                                                      
    
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  • 2. Finding a Shipping Fee

    The table shows an online store's shipping rates. You order a 330-pound weight set with 2-day shipping. What is the shipping fee? (See Example 1 and Example 2.)

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    __    __     ___      ______     ___     _____    
    \ \\ / //   / _ \\   /_____//   / _ \\  |  __ \\  
     \ \/ //   / //\ \\  `____ `   | / \ || | |  \ || 
      \  //   |  ___  || /___//    | \_/ || | |__/ || 
       \//    |_||  |_|| `__ `      \___//  |_____//  
        `     `-`   `-`  /_//       `---`    -----`   
                         `-`                          
    
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  • 3. Comparing Fees for Different Delivery Times

    The table shows an online store's shipping rates. You order a 26-pound television. Suppose you use 3-5 day shipping instead of 2-day shipping. How much will you save? (See Example 1 and Example 2.)

    • Worked-Out Solution

      Begin by finding the shipping fee for each delivery time.

      By using the slower delivery time, you will save

      Shipping rates vary a lot. When you are shipping a package, you can save money by:

      1. using a longer delivery time.
      2. wrapping the package yourself.
      3. using a shipping rate comparison site, such as www.ShippingSideKick.com, on the Internet.
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     __   __    _____    _    _      ___      _____   
     \ \\/ //  |  ___|| | \  / ||   / _ \\   |__  //  
      \   //   | ||__   |  \/  ||  / //\ \\    / //   
      / . \\   | ||__   | .  . || |  ___  ||  / //__  
     /_//\_\\  |_____|| |_|\/|_|| |_||  |_|| /_____|| 
     `-`  --`  `-----`  `-`  `-`  `-`   `-`  `-----`  
                                                      
    
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  • 4. Comparing Prices for Different Delivery Times

    The table shows an online store's shipping rates. You order a 119-pound couch. Suppose you use 1-day shipping instead of 3-5 day shipping. How much more will you pay? (See Example 1 and Example 2.)

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                _____     ______   _    _    ______   
        ___    |  ___||  /_____// | || | || |      \\ 
       /   ||  | ||__    `____ `  | || | || |  --  // 
      | [] ||  | ||__    /___//   | \\_/ || |  --  \\ 
       \__ ||  |_____||  `__ `     \____//  |______// 
        -|_||  `-----`   /_//       `---`   `------`  
         `-`             `-`                          
    
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  • 5. Buy Online or Buy Locally

    The table shows an online store's shipping rates. You wait until the last minute to buy a 159-pound treadmill for a birthday present. The online price of the treadmill is $110 less than the price of the same treadmill at a local fitness store. You need the treadmill by tomorrow, so you will have to pay for 1-day shipping. (See Example 1 and Example 2.)

    1. Estimate the shipping fee for the treadmill.
    2. Will it cost more to order the treadmill online with 1-day shipping or to buy the treadmill at the local fitness store?
    3. Does your answer to part (b) change if you had an extra day to place your order? What if you had an extra week?
    • Worked-Out Solution
      1. The shipping fee for 1-day delivery is

      2. Even though the fitness store price is $110 more, with a shipping fee of $300.51, it costs more to order the treadmill online with 1-day shipping.

      3. The shipping fee for 2-day delivery is

        The fitness store price is still lower. This assumes that the local fitness store does not charge for delivery.

        The shipping fee for 3-5 day delivery is

        If you had an extra week, then it will cost more to buy the treadmill at a local fitness store.

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      ______   __   __    _  _      ___      ______  
     /_____//  \ \\/ //  | \| ||   / _ \\   /_   _// 
     `____ `    \ ` //   |  ' ||  | / \ ||    | ||   
     /___//      | ||    | .  ||  | \_/ ||   _| ||   
     `__ `       |_||    |_|\_||   \___//   /__//    
     /_//        `-`'    `-` -`    `---`    `--`     
     `-`                                             
    
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  • 6. Determining Reasonable Shipping Charge

    The table shows an online store's shipping rates. You recently purchased a pair of headphones online. The shipping fee was $12.24. You believe that you were overcharged for 3-5 day shipping but the weight of the headphones is not listed on the receipt. (See Example 1 and Example 2.)

    1. How much do the headphones have to weigh for the fee to be correct? Is the weight reasonable?

    2. If the weight is not reasonable, write an e-mail to the store explaining the error and asking for a refund.

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     _    _     _____     _____     ______   __   __  
    | |  | ||  |  ___||  |__  //   /_   _//  \ \\/ // 
    | |/\| ||  | ||__      / //     -| ||-    \   //  
    |  /\  ||  | ||__     / //__    _| ||_    / . \\  
    |_// \_||  |_____||  /_____||  /_____//  /_//\_\\ 
    `-`   `-`  `-----`   `-----`   `-----`   `-`  --` 
                                                      
    
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