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Question

a 129-inch ribbon is to be cut into 3 pieces. the longest piece is to be 36 inches longer than the shortest piece and the third piece is half the length of the longest piece. what is the length of each piece?

Answer 1

Let x = the length of the shortest piece of ribbon

 

The longest piece is 36 inches longer than the shortest piece = x+36

 

The third piece is half the length of the longest piece = (x+36)/2 = x/2 + 18

 

129 inches = x + (x + 36) + (x/2 + 18)

 

129 = 5x/2 + 54

 

75 = 5x/2

 

150 = 5x

 

Solve for x, the length of the shortest piece.  Once you have x, the other pieces are (x+36) and (x/2+18).  Check your work by adding the three lengths together to be sure they add up to 129.

Answer 2

Hi Brittany,

 

Let's set it up: R₁ + R₂ +R₃ = 129 (R for ribbon)

 

Let's say R₁ is the longest, R₂ is second longest (3rd piece), and R₃ is the shortest.

 

The longest piece (R₁) = 36 + R3 (shortest) and (R₂) (3rd piece) = (R₁) / 2.

 

So, rewrite the equation: (36 + R₃) + (36 + R₃) / 2 + R₃ = 129.

                                                          

                                          R₁      +       R₂      + R₃ = 129.

 

And as you combine like terms, you will get   36 +     (2)(R₃)      +   36 + R_{3 / 2} = 129.

                                                                       (combined R1 & R3)         

 

Subtract 36 for both sides and you should get: (2)R₃  +  36 + R₃  = 93

                                                                                      2

 

To get rid-of the 2 from denominator, multiply by 2 on both sides.  And you should get 4*R₃ + 36 + R₃ = 186.

 

As you combine like terms again and subtract 36 for both sides, you should get 5 * R₃ = 150.  Divide by 5 for both sides to get R₃ by itself and you should get R₃ = 30.  So, shortest ribbon is 30 inches long.

 

Let's put that value into the original problem.  The longest piece (R₁) is 36 inches longer than shortest one.  So, you will have 30+36 = 86 for R₁ (longest ribbon).  And then second longest (R₂) is half of the longest.  So, 66÷2 and you should get 33 for (R₂).

 

Let's check it.  R₁ = 66, R₂ = 33. R₃ = 30.  66+33+30 = 129 inches.  It checks out.

 

Good luck.