Question

A 33​-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first​ piece, and the third piece is three inches more than seven times the length of the first piece. Find the lengths of the pieces.

Answer 1

Answer: the length of the first piece is 3 inches.

the length of the second piece is 6 inches.

the length of the third piece is 24 inches.

Step-by-step explanation:

Let x represent the length of the first piece of stick.

Let y represent the length of the second piece of stick.

Let z represent the length of the third piece of stick.

The total length of the stick is 33 inches. This means that

x + y + z = 33 - - - - - - - - - - - - 1

The second piece is twice as long as the first​ piece. This means that

y = 2x

The third piece is three inches more than seven times the length of the first piece. This means that

z = 7x + 3

Substituting y = 2x and z = 7x + 3 into equation 1, it becomes

x + 2x + 7x + 3 = 33

10x + 3 = 33

10x = 33 - 3 = 30

x = 30/10 = 3

y = 2x = 2 × 3

y = 6

z = 7x + 3 = 7 × 3 + 3

z = 24