Find the length of the shorter piece.

Question

77 cm long is cut into three pieces such that the second piece is twice as long as the first and the third is 2 cm longer than the second.
Find the length of the shorter piece.

Answer 1

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.

Answer 2

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