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1.1 Order of Operations & Formulas

1.1 Order of Operations & Formulas
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  • 7. Finding the Total Cost of Parking

    You buy a campus parking permit for $250. During the year, you get four $15 parking tickets. Which of the following keystroke sequences is better for finding your total parking cost? Explain your reasoning. (See Example 3.)

    • Worked-Out Solution

      To find the total parking cost, add the cost of a campus parking permit to the cost of four parking tickets. When deciding which keystroke sequence is better, standard order of operations tells you to do operations in parentheses first.

      1. This keystroke sequence tells the calculator to add 250 and 4 first and then multiply by 15. This is not correct.

        (250 + 4) x 15 = 250 + 60 = 310

      2. This keystroke sequence tells the calculator to multiply 4 and 15 first and then add 250. This is correct.

        250 + (4 x 15) = 250 + 60 = 310

        Your total parking cost is $310.

        Always Check for Reasonableness of Your Answer

        Incorrect keystroke sequences often produce unreasonable answers. Whenever you use a calculator to perform calculations, ask yourself whether the displayed answer makes sense in the context of the problem.

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      ____      ______    ______     ___      ______  
     |  _ \\   /_   _//  /_____//   / _ \\   /_   _// 
     | |_| ||   -| ||-   `____ `   | / \ ||    | ||   
     | .  //    _| ||_   /___//    | \_/ ||   _| ||   
     |_|\_\\   /_____//  `__ `      \___//   /__//    
     `-` --`   `-----`   /_//       `---`    `--`     
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  • 8. Finding the Average Cost of Books

    Your books for this semester cost $95, $120, and $115. Which of the following keystroke sequences is better for finding the average book cost? Explain your reasoning. (See Example 3.)

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      ______    _____     _____    _    _    _    _   
     /_   _//  |  ___||  /  ___|| | || | || | |  | || 
       | ||    | ||__   | // __   | || | || | |/\| || 
      _| ||    | ||__   | \\_\ || | \\_/ || |  /\  || 
     /__//     |_____||  \____//   \____//  |_// \_|| 
     `--`      `-----`    `---`     `---`   `-`   `-` 
                                                      
    
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  • 9. Finding the Total Cost of the Pizza Party

    You buy 3 pizzas for $10 each and 5 bottles of cola for $2 each. Which of the following keystroke sequences is better for finding the total cost? Explain your reasoning. (See Example 3.)

    • Worked-Out Solution

      To find the total cost, add the cost of 3 pizzas to the cost of 5 bottles of cola.

      1. This keystroke sequence is better. By using parentheses, you are forcing the calculator to multiply twice before you add.

        (3 x 10) + (5 x 2) = 30 + 10 = 40

        Your total cost is $40.

      2. On a calculator that follows the conventional order of operations, this keystroke sequence also tells the calculator to add 30 and 10. However, on a calculator that is "operation activated," this sequence tells the calculator to multiply 3 and 10, add 5, then multiply by 2. This is not correct.

        (3 x 10) + 5 x 2 = 30 + 5 x 2 = 35 + x 2 = 70

        Always Check for Reasonableness of Your Answer

        Incorrect keystroke sequences often produce unreasonable answers. Whenever you use a calculator to perform calculations, ask yourself whether the displayed answer makes sense in the context of the problem.

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      ______   __   __    _____      ___      _  __  
     /_   _//  \ \\/ //  |__  //    / _ \\   | |/ // 
       | ||     \ ` //     / //    | / \ ||  | ' //  
      _| ||      | ||     / //__   | \_/ ||  | . \\  
     /__//       |_||    /_____||   \___//   |_|\_\\ 
     `--`        `-`'    `-----`    `---`    `-` --` 
                                                     
    
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  • 10. Finding the Value of a Car

    A new car worth $25,000 depreciates at a rate of 50% every 3 years. The value of the car after 6 years is 25,000(0.5 squared) Which of the following keystroke sequences is better for finding the value of the car? Explain your reasoning. (See Example 3.)

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      _____      ___                ______   _    _   
     |__  //    / _ \\    ____     /_   _// | \  / || 
       / //    / //\ \\  |    \\    -| ||-  |  \/  || 
      / //__  |  ___  || | [] ||    _| ||_  | .  . || 
     /_____|| |_||  |_|| |  __//   /_____// |_|\/|_|| 
     `-----`  `-`   `-`  |_|`-`    `-----`  `-`  `-`  
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  • 11. Finding the Cost of Seeding a Football Field

    You are buying lawn seed for the football field. A 10-pound bag of lawn seed covers 2000 square feet. (See Example 4.)

    1. How many 10-pound bags of lawn seed should you buy?
    2. A 10-pound bag of lawn seed costs $27.79. What is the total cost of your purchase?

    • Worked-Out Solution
      1. Begin by finding the area of the football field.

        Area equals length times width equals 360 feet times 160 feet equals 57,600 square feet

        Because a 10-pound bag covers 2000 square feet, divide the area by 2000 to find the number of 10-pound bags you need.

        57,600 square feet divided by 2000 square feet divided by 1 bag = 28.8 bags

        You should buy 29 bags --- perhaps 30 bags to account for overlap and waste.

      2. Each bag costs $27.79. Multiply this price by the number of bags to find the total cost.

          $27.79 divided by 1 bag times 29 bags = $805.91

        The total cost is about $806. If you buy 30 bags, then the total cost is about $834.

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     _    _      ___     ______     ______    _____   
    | \  / ||   / _ \\  |      \\  /_   _//  |__  //  
    |  \/  ||  | / \ || |  --  //   -| ||-     / //   
    | .  . ||  | \_/ || |  --  \\   _| ||_    / //__  
    |_|\/|_||   \___//  |______//  /_____//  /_____|| 
    `-`  `-`    `---`   `------`   `-----`   `-----`  
                                                      
    
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    system user
    Cody (moderator)6 years ago |
    The correct answer could be 29 or 30. In Quantitative Literacy, the goal is to think about the answer in terms of the real world. If a landscaper were buying lawn seed he or she would want to take into consideration the fact that some of the seeds might overlap, and therefore buy enough seeds to account for this possibility. However, strictly speaking mathematically, 29 would be a correct answer, because that is enough bags to cover the field almost exactly.
    I see how this could have been a confusing solution though, and thank you for asking the question. That's the great thing about this new book.
    If you have any more questions feel free to leave a comment.
    0
    system user
    Guest   6 years ago |
    Somewhat confusing to have decided on 30 bags - some of my students aren't sure then what to put.
    0
  • 12. Finding the Amount of Paint Needed

    Latex paint is used to paint the end zones of the football field. Each gallon of paint must be diluted with 1 gallon of water. One gallon of diluted latex paint covers 100 square feet. (See Example 4.)

    1. Each end zone is 30 feet long. How many gallons of undiluted latex paint are needed to paint both end zones?
    2. Why do you think the paint is diluted?

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