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A 41​-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 one inch more than five times the length of the first piece. Find the lengths of the pieces.

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Answer:

Length of first piece = 5 inches

Length of second piece = 10 inches

Length of third piece = 26 inches

Step-by-step explanation:

Given that:

Length of piece of steel = 41 inch

Let,

x be the length of first piece

y be the length of second piece

z be the length of third piece

According to given statement;

x+y+z = 41          Eqn 1

y = 2x                Eqn 2

z = 5x+1            Eqn 3

Putting value of y and z from Eqn 2 and 3 in Eqn 1

[tex]x+2x+5x+1=41\\8x = 41-1 \\8x = 40[/tex]

Dividing both sides by 8

[tex]\frac{8x}{8}=\frac{40}{8}\\x=5[/tex]

Putting x=5 in Eqn 2 and 3

y = 2(5) = 10

z = 5(5) + 1 = 25+1 = 26

Hence,

Length of first piece = 5 inches

Length of second piece = 10 inches

Length of third piece = 26 inches

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