a 25 inch piece of a steel rod is cut into 3 pieces so that the length of the second piece is twice the length of the first piece.The third piece is 1 inch longer than 5 times the length of the first piece.What are the lengths of the pieces
Let's call the first piece of rod X:
X+2X+(5X+1)=25
8X+1=25
8X+1-1=25-1
8X=24
(8X)÷8=24÷8
X=3
Son we know the first piece is 3 inches. The second piece is 2X, so 2×3 is 6. The third piece is 5X+1, so 5(3)+1 is 16. To check the values, if you add them together you should get the length of the original rod. 3+6+16=25, so the three pieces are 3, 6, and 16 inches long.
Thank You
To find the lengths of the three pieces, let's assign variables to represent their lengths.
Let's say the length of the first piece is x inches.
According to the information given, the length of the second piece is twice the length of the first piece. Therefore, the length of the second piece is 2x inches.
The length of the third piece is 1 inch longer than 5 times the length of the first piece. So, the length of the third piece is 5x + 1 inches.
Now, since the total length of the rod is 25 inches, we can write an equation:
x + 2x + (5x + 1) = 25
Simplifying the equation, we combine like terms:
8x + 1 = 25
Next, we isolate x by subtracting 1 from both sides:
8x = 24
Then, we divide by 8 to solve for x:
x = 3
Now that we have found the value of x, we can substitute it back into our equations to find the lengths of the three pieces.
The length of the first piece is x = 3 inches.
The length of the second piece is 2x = 2 * 3 = 6 inches.
The length of the third piece is 5x + 1 = 5 * 3 + 1 = 16 inches.
Therefore, the lengths of the three pieces are 3 inches, 6 inches, and 16 inches, respectively.