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1.1 Order of Operations & Formulas

1.1 Order of Operations & Formulas
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  • 1. Equal-Payment Plan for Natural Gas Bills

    From October through August, on an equal-payment plan, you pay $50 each month on your gas bill. How much do you owe in September? (See Example 1.)

    data

    • Worked-Out Solution

      Add the 12 monthly usage amounts and subtract the 11 equal payments already made to find the amount you owe in September.

      Equation 1

      You owe $47.08 in September.

      Try downloading the spreadsheet with the data. Check your answer by entering $50.00 as the monthly payment.

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       _____   __   __   _    _    __   __   _    _   
      / ___//  \ \\/ // | \  / ||  \ \\/ // | \  / || 
      \___ \\   \ ` //  |  \/  ||   \ ` //  |  \/  || 
      /    //    | ||   | .  . ||    | ||   | .  . || 
     /____//     |_||   |_|\/|_||    |_||   |_|\/|_|| 
    `-----`      `-`'   `-`  `-`     `-`'   `-`  `-`  
                                                      
    
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    Ron Larson (author)7 years ago |
    Throughout this book, the lessons always have 6 pages. The exercises sets always have 4 pages and are correlated to the examples as follows:

    1st page of exercises: Examples 1 and 2
    2nd page of exercises: Examples 3 and 4
    3rd page of exercises: Examples 5 and 6
    4th page of exercises: Extends the concepts in Examples 1-6
    0
  • 2. Equal-Payment Plan for Natural Gas Bills

    You are on an equal-payment plan. What is the least amount that you can pay each month from October through August to owe nothing in September? (See Example 1.)

    data

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      _  _     _____    _    _     _____     ____    
     | \| ||  |  ___|| | \  / ||  |  ___||  |  _ \\  
     |  ' ||  | ||__   |  \/  ||  | ||__    | |_| || 
     | .  ||  | ||__   | .  . ||  | ||__    | .  //  
     |_|\_||  |_____|| |_|\/|_||  |_____||  |_|\_\\  
     `-` -`   `-----`  `-`  `-`   `-----`   `-` --`  
                                                     
    
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    Jackie (moderator)5 years ago |
    The worked-out solutions are only available for odd-numbered problems, so unfortunately we cannot show the work for this exercise.
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    system user
    Guest   5 years ago |
    show the work
    2
  • 3. Equal-Payment Plan for Electric Bills
    From January through November, on an equal-payment plan, you pay $75 each
    month on your electric bill. How much do you owe in December? (See Example 1.)

    • Worked-Out Solution

      Add the 12 monthly usage amounts and subtract the 11 equal payments already made to find the amount you owe in December.

      Equation

      You owe $39.41 in December.

      Try downloading the spreadsheet with the data. Check your answer by entering $75.00 as the monthly payment.

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      _  __     ___     _    _    __   __   ______   
     | |/ //   / _ \\  | \  / ||  \ \\/ // |      \\ 
     | ' //   | / \ || |  \/  ||   \ ` //  |  --  // 
     | . \\   | \_/ || | .  . ||    | ||   |  --  \\ 
     |_|\_\\   \___//  |_|\/|_||    |_||   |______// 
     `-` --`   `---`   `-`  `-`     `-`'   `------`  
                                                     
    
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  • 4. Equal-Payment Plan for Electric Bills

    You are on an equal-payment plan. What is the least amount that you can pay each month from January through November to owe nothing in December? (See Example 1.)

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      _____    __   __    _____      ___      ____    
     /  ___||  \ \\/ //  |__  //    / _ \\   |  _ \\  
    | // __     \ ` //     / //    | / \ ||  | |_| || 
    | \\_\ ||    | ||     / //__   | \_/ ||  | .  //  
     \____//     |_||    /_____||   \___//   |_|\_\\  
      `---`      `-`'    `-----`    `---`    `-` --`  
                                                      
    
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  • 5. Calories in Pink Lemonade

    There are 774 calories in a cup of sugar, 65 calories in a cup of fresh lemon juice, and 137 calories in a cup of cranberry juice. (See Example 2.)

    1. How many calories are in the old-fashioned pink lemonade recipe?
    2. This recipe makes nine servings. How many calories are in one serving?

    • Worked-Out Solution
      1. To obtain the number of calories in the recipe, first, multiply the number of calories in a cup by the number of cups. Then, add.

        Equation for finding total calories

        There are about 1360 calories in the recipe.

        Fraction Conversion Help

      2. Divide the number of calories by the number of servings to get the number of calories per serving.

        There are about 150 calories per serving.

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    __    __   _    _   __    __     ___              
    \ \\ / // | || | || \ \\ / //   / _ \\    ____    
     \ \/ //  | || | ||  \ \/ //   | / \ ||  |    \\  
      \  //   | \\_/ ||   \  //    | \_/ ||  | [] ||  
       \//     \____//     \//      \___//   |  __//  
        `       `---`       `       `---`    |_|`-`   
                                             `-`      
    
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  • 6. Calories in Fudge

    There are 99 calories in an ounce of cream cheese, 12 calories in a teaspoon of vanilla extract, 389 calories in a cup of powdered sugar, and 145 calories in a square of chocolate. Salt has 0 calories.
    (See Example 2.)

    1. How many calories are in the fudge recipe?
    2. This recipe uses an 8-inch by 8-inch dish. How many calories are in a 1-inch by 1-inch piece of fudge?

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      _  _    _    _     _____    _    _    __   _   
     | \| || | || | ||  |__  //  | || | || | || | || 
     |  ' || | || | ||    / //   | || | || | '--' || 
     | .  || | \\_/ ||   / //__  | \\_/ || | .--. || 
     |_|\_||  \____//   /_____||  \____//  |_|| |_|| 
     `-` -`    `---`    `-----`    `---`   `-`  `-`  
                                                     
    
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