Answer:
The length of the first piece is 4, the length of the second piece is 8 and the length of the third piece is 19
Explanation:
A 31-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 four times the length of the first piece.
To solve this, we need to write the mathematical statement.
Let x, y, and z equal to the length of the first, second and the third piece respectively
From the first statement;"A 31-inch piece of steel is cut into three pieces", this can be represented mathematically as x + y + z = 31------------------(1)
The next statement is; "so that the second piece is twice as long as the first piece", this can be represented mathematically as y= 2x------------------------(2)
The next statement is;"the third piece is three inches more than four times the length of the first piece", this can be mathematically written as z=3+4x--------------------------------(3)
We can now proceed to solve
substitute equation (2) and (3) into equation (1)
x + y + z = 31
x + 2x + 3+4x=31
7x + 3 = 31
subtract 3 from both-side of the equation
7x + 3-3 = 31-3
7x =28
Divide both-side of the equation by 7
7x/7 = 28/7
x = 4
Substitute x=7 in equation (2) to get the value of y
y=2x
y = 2(4)
y = 8
Substitute x=4 in equation (3) to get the value of z
z= 3+4x
z=3+4(4)
z=3+16
z=19
Therefore x=4 y=8 and z=19
The length of the first piece is 4, the length of the second piece is 8 and the length of the third piece is 19