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Evgen [1.6K]
3 years ago
15

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. Find the lengths of the pieces.
Mathematics
2 answers:
Nostrana [21]3 years ago
6 0

Answer:

The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

Step-by-step explanation:

Total length of the steel = 31 inches

Let the length of the first piece = x

let the length of the second piece = y

Let the length of the third piece = z

So,    

  y = 2x

  z = 4x + 3

x + 2x + 4x +3  = total length of the steel = 31

   7x + 3 + 31

    7x = 31 - 3

    7x = 28

    x= 4 inches

Thus; y = 2x = 2 × 4 = 8 inches

         z = 4x +3 = 4×4 +3 =19 inches

∴The length of the first piece is 4 inches, that of the second is 8 inches and the third 19 inches.

sergij07 [2.7K]3 years ago
4 0

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

Step-by-step explanation:

<u><em>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.</em></u>

<u><em /></u>

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

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