Question

A 25-foot piece of steel is cut into three pieces so that the first piece is twice as long as the second piece, and the third piece is five feet less than three times the length of the second piece. Find the lengths of the pieces.

a) 5 ft, 10 ft, 10 ft
b) 10 ft, 5 ft, 10 ft
c) 15 ft, 5 ft, 5 ft
d) 5 ft, 15 ft, 5 ft

Answer 1

After setting up equations based on the problem statement, we find that the second piece of steel measures 5 feet, the first is twice its length at 10 feet, and the third is 5 feet less than three times the second piece, also measuring 10 feet. The correct lengths are therefore 10 feet, 5 feet, and 10 feet respectively.

Step-by-step explanation:

To find the lengths of the three pieces of steel, we need to set up equations based on the information given. Let's denote the second piece's length as x, the first piece's length as 2x (twice the second piece), and the third piece's length as 3x - 5 feet (five feet less than three times the length of the second piece).

Accordingly, the total length of the three pieces of steel is the sum of the lengths of these pieces:

1. First piece + Second piece + Third piece = Total length
2. 2x + x + (3x - 5) = 25 feet
3. 6x - 5 = 25
4. 6x = 30
5. x = 5 feet

Using the value of x, we can now determine the lengths of each piece:

• First piece = 2x = 2(5 feet) = 10 feet
• Second piece = x = 5 feet
• Third piece = 3x - 5 = 3(5 feet) - 5 feet = 15 feet - 5 feet = 10 feet

Therefore, the lengths of the pieces are 10 feet, 5 feet, and 10 feet respectively, which corresponds to option (b) 10 ft, 5 ft, 10 ft.