Question

A 33-inch piece of steel is cut into three pieces so that the second piece is twiceas long as the first piece, and the third piece is one inch more than five times thelength of the first piece. What is the length of the first piece?

Answer 1

Let;

x = the length of the first piece

y=the length of the second piece

z=the length of the third piece

From the question;

"the second piece is twice as long as the first piece" can be written in equation as:

y = 2x

"the third piece is one inch more than five times the length of the first piece"

can be written as :

z= 5x+ 1

Total length of the 3 pieces = 33

This implies:

x + y + z =33

substitute y=2x and z=5x+1 into the above

x + 2x + 5x+1 = 33

8x + 1 = 33

subtract 1 from both-side of the equation

8x = 33 -1

8x = 32

divide both-side of the equation by 8

x= 32/8

x= 4

The length of the first piece is 4-inches