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Math - Length of Ribbon Needed










































Calculate Length of Ribbon Needed

   • Joyce is making bows for wreaths

           i. She has 5 yards (or 60 ft) of ribbon to start

           ii. She needs 1 ⅔ of ribbon for each bow

       A. How many feet of ribbon will Joyce have left if she makes 10 bows?

       B. How many feet of ribbon will Joyce have left if she makes 15 ribbons?

       C. Define a variable for that amount of bows that Joyce makes then use the variable to write an expression that represents the length of ribbon that Joyce has left given the number of bows she has made.

       D. How many bows has Joyce made if she has 10ft of ribbon left.

       E. Use a complete sentence to explain how you found that answer to part d

       F. Write an equation that you can use to find the amount of bows Joyce will have made if she has 25 ft of ribbon left


Comments for Math - Length of Ribbon Needed

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Aug 31, 2012
Equation for Length of Ribbon
by: Staff


Answer:

Part I


A. How many feet of ribbon will Joyce have left if she makes 10 bows?

    Known Information

       - Joyce is making wreaths.

       - Joyce will be making the bows for each wreath.

       - Joyce has 5 yards, or 60 feet of ribbon to start.

       - Joyce will use 1 ⅔ feet of ribbon for each bow.


    Unknown Information

       - Number of feet of ribbon left over


   • Write (or rewrite) the known and unknown information using mathematical notation (rather than sentences)

          n = number of bows = 10

          b = ribbon used per bow = 1 ⅔ feet

          r = total number of feet of ribbon available = 60 feet

          x = number of feet of ribbon left over after making bows = unknown


     The equation for the number of feet of ribbon left over is:

          x = total ribbon available - total ribbon used

          x = r - (n * b)



     Solve for x

          x = r - (n * b)


     Substitute the known values for the variables

          x = 60 - [10 * (1 ⅔)]


     convert the mixed number 1 2/3 to an improper fraction

          x = 60 - [10 * (5/3)]


     multiply 10 * (5/3)

          x = 60 – [10 * (5/3)]

          x = 60 - (50/3)


     convert 60 to an improper fraction with a denominator of 3

          x = (180/3) - (50/3)

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Aug 31, 2012
Equation for Length of Ribbon
by: Staff


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Part II

     subtract the two fractions

          x = (180 - 50)/3

          x = (130)/3

          x = 130/3


     divide 130 by 3

          x = 43 r 1

          x = 43 ⅓ feet


     the final answer is:

          Number of feet of ribbon left over = 43 ⅓ feet

--------------------------------------------------------

     Check the answer

       Substitute all known values into the original equation:


          x = r - (n * b)

          43 1/3 = 60 - [10 * (1 2/3)]

          43 1/3 = 60 - [10 * (5/3)]

          43 1/3 = 60 - (50/3)

          43 1/3 = (180/3) - (50/3)

          43 1/3 = (180 - 50)/3

          43 1/3 = 130/3

          43 1/3 = 43 1/3, correct

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B. How many feet of ribbon will Joyce have left if she makes 15 ribbons?


     The equation for the number of feet of ribbon left over is:

          x = total ribbon available - total ribbon used

          x = r - (n * b)



     Solve for x

          x = r - (n * b)


     Substitute the known values for the variables

          x = 60 - [15 * (1 ⅔)]

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Aug 31, 2012
Equation for Length of Ribbon
by: Staff


-------------------------------------------------------

Part III


     convert the mixed number 1 2/3 to an improper fraction

          x = 60 - [15 * (5/3)]


     multiply 15 * (5/3)

          x = 60 – [15 * (5/3)]

          x = 60 - (75/3)


     convert 60 to an improper fraction with a denominator of 3

          x = (180/3) - (75/3)


     subtract the two fractions

          x = (180 - 75)/3

          x = (105)/3

          x = 105/3


     divide 105 by 3

          x = 35 feet


     the final answer is:

          Number of feet of ribbon left over = 35 feet

--------------------------------------------------------

     Check the answer

       Substitute all known values into the original equation:


          x = r - (n * b)

          35 = 60 - [15 * (1 2/3)]

          35 = 60 - [15 * (5/3)]

          35 = 60 - (75/3)

          35 = (180/3) - (75/3)

          35 = (180 - 75)/3

          35 = 105/3

          35 = 35, correct

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Aug 31, 2012
Equation for Length of Ribbon
by: Staff


--------------------------------------------------------

Part IV


C. Define a variable for that amount of bows that Joyce makes then use the variable to write an expression that represents the length of ribbon that Joyce has left given the number of bows she has made.

          n = number of bows

          b = ribbon used per bow = 1 ⅔ feet

          r = total number of feet of ribbon available = 60 feet

          x = number of feet of ribbon left over after making bows = unknown


     The equation for the number of feet of ribbon left over is:

          x = total ribbon available - total ribbon used

          x = r - (n * b)


     the final answer is:

          x = r - (n * b)


D. How many bows has Joyce made if she has 10 ft of ribbon left?


     Solve for “n”

          x = r - (n * b)


     Substitute the known values for the variables

          10 = 60 - (n * 1 ⅔)


     convert the mixed number 1 2/3 to an improper fraction

          10 = 60 - [n * (5/3)]


     multiply n * (5/3)

          10 = 60 - (5n/3)

     convert 60 to an improper fraction with a denominator of 3

          10 = (180/3) - (5n/3)


     subtract the two fractions

          10 = (180 - 5n)/3

     multiply each side of the equation by 3


--------------------------------------------------------

Aug 31, 2012
Equation for Length of Ribbon
by: Staff


--------------------------------------------------------

Part V


          10*3 = [(180 - 5n)/3]*3

          30 = [(180 - 5n)*(3/3)]

          30 = [(180 - 5n)*(1)]

          30 = (180 - 5n)

          30 = 180 - 5n



     add 5n to each side of the equation

          30 + 5n = 180 - 5n + 5n

          30 + 5n = 180 +0

          30 + 5n = 180


     subtract 30 from each side of the equation

          30 - 30 + 5n = 180 - 30

          0 + 5n = 180 - 30

          5n = 180 - 30

          5n = 150


     divide each side of the equation by 5

          5n = 150

          5n / 5 = 150 / 5

          n * (5 / 5) = 150 / 5

          n * (1) = 150 / 5

          n = 150 / 5

          n = 30

     the final answer is:

          Number ribbons = 30 ribbons



E. Use a complete sentence to explain how you found that answer to part d

     I solved for “n” using the equation shown in part C.


F. Write an equation that you can use to find the amount of bows Joyce will have made if she has 25 ft of ribbon left


          x = r - (n * b)


     Substitute the known values for the variables

          25 = 60 - (n * 1 ⅔)


     the final answer is:

          25 = 60 - (n * 1 ⅔)



Thanks for writing.

Staff
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