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Find the length of the shorter piece.

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2 Answers

Assign variables to each piece:

     1st piece = x

     2nd piece = y

     3rd piece = z

We are given that the total length of these three pieces is 77 cm:     x + y + z = 77

Since we are given that the 2nd piece (y) is twice as long as the first piece (x), then we arrive at the following:     y = 2x

Also, we are given that the 3rd piece (z) is 2 cm longer than the second piece (y). This leads us to the following:     z = y + 2     ==>     z = 2x + 2

Now, we substitute what we've found y and z to equal into the original equations. That is,

     x + y + z = 77

     x + (2x) + (2x + 2) = 77

     x + 2x + 2x + 2 = 77

After we combine the like terms on the left hand side of the equation, we get the following:

     5x + 2 = 77

Subtract 2 from both sides of the equation:

     5x + 2 - 2 = 77 - 2

     5x = 75

Divide both sides of the equation by 5 to solve for x:

     5x/5 = 75/5

     x = 15

Therefore,

     1st piece = x = 15 cm

     2nd piece = y = 2x = 2·15 = 30 cm

     3rd piece = z = 2x + 2 = 2·15 + 2 = 30 + 2 = 32 cm

Thus, the shortest piece is the 1st piece with a length of 15 cm.

You have a total length and then descriptions of the component pieces so just let

x = the shortest piece

2x =the "middle" piece

2x + 2 = the longest piece

Now just add them up and solve

x + 2x + 2x + 2 = 77

5x = 75

x = 15 cm

the remaining two pieces are 30 cm and 32 cm respectively

add them all up to check your work

15 + 30 + 32 = 77

77 = 77