  # 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

 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) -------------------------------------------------------

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

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

 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 www.solving-math-problems.com

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