a 38 inch piece of steels 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 four times the length of the first piece. find the lengths of pieces.
please show how you got 38 for the answer
Let's assume the length of the first piece is x inches.
According to the information given, the second piece is twice as long as the first piece. So, the length of the second piece is 2x inches.
The third piece is three inches more than four times the length of the first piece. So, the length of the third piece is 4x + 3 inches.
The sum of the lengths of all three pieces is equal to the length of the steel piece, which is 38 inches.
Therefore, we can write the following equation:
x + 2x + 4x + 3 = 38
Combining like terms:
7x + 3 = 38
Subtracting 3 from both sides:
7x = 35
Dividing by 7:
x = 5
So, the length of the first piece is 5 inches.
The length of the second piece is twice the length of the first piece, which is 2 * 5 = 10 inches.
The length of the third piece is three inches more than four times the length of the first piece, which is 4 * 5 + 3 = 23 inches.
Therefore, the lengths of the three pieces are: 5 inches, 10 inches, and 23 inches.
To find the lengths of the three pieces, let's assign variables to represent the lengths of the pieces.
Let 'x' be the length of the first piece.
The second piece is twice as long as the first piece, so its length is '2x'.
The third piece is three inches more than four times the length of the first piece, so its length is '4x + 3'.
According to the problem, the sum of the three pieces is equal to 38 inches:
x + 2x + 4x + 3 = 38
Combining like terms:
7x + 3 = 38
Subtracting 3 from both sides of the equation:
7x = 35
Dividing both sides of the equation by 7:
x = 5
Now that we have the length of the first piece, we can find the lengths of the second and third pieces:
The length of the second piece: 2x = 2(5) = 10
The length of the third piece: 4x + 3 = 4(5) + 3 = 20 + 3 = 23
Therefore, the lengths of the three pieces are:
First piece: 5 inches
Second piece: 10 inches
Third piece: 23 inches
first piece --- x
second piece --- 2x
third piece --- 4x+3
solve x + 2x + 4x+3 = 38
it is easy.