Answer:
The shortest piece is the first piece and it is 14 cm long.
Step-by-step explanation:
We have three unknowns so we need 3 equations.
Let x = the length of the first piece
Let y = the length of the second piece
Let z = the length of the third piece.
x + y + z = 74 y = 2x z = y + 4
There are a number of ways to solve this. I am going to plug in 2x for y into the first and the third equation to get:
x + y + z = 74
x + 2x + z = 74 Combine the x terms
3x + z = 74
Next, I am going to substitute 2x in for y in the third equation above.
z = y + 4
z = 2x + 4 I am going to put both variable on the left side of the equation
z - 2x = 4
I can know take the two bold equations that I have above and solve for the either x or z. I am going to solve for z. I need one of the equation to have a z and the other equation to have -z so that they will cancel one another out. I am going to multiple z - 2x = 4 all the way through by -1 to get:
z - 2x = 4
-1(z - 2x) = 4(-1)
-z +2x = -4
I am going to rearrange 3x + z = 74 so that the z term is first and add it to -z + 2x = -4
z + 3x = 74
<u>-z + 2x = -4</u>
5x = 70 divide both sides by 5
x = 14 This is the length of the first piece.
y = 2x
y = 2(14) = 28
y = 28 This is the length of the second piece.
z = y+4
z = 28 + 4 = 32
or
x + y + z = 74
14 + 28 + z = 74
42 + z = 74 Subtract 42 from both sides.
z = 32
