Question

A piece of wire 16 m long is cut
into two pieces so that one piece
is three fifths as long as the other. Find the length of each piece.

Answers

  1. Answer:
    The longer piece is 10 m, and the shorter piece is 6 m.
    Step-by-step explanation:
    16 / (5 + 3) = 2 m
    2 x 5 = 10 m
    2 x 3 = 6 m

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  2. After constructing and solving the linear equation x+\frac{3}{5}x=16, we obtain that the shorter piece of the wire is 6 m long whereas the longer piece is 10 m long.

    What is a linear equation?

    • An equation consisting of one or more variables and constants with some mathematical operation (such as Addition, Subtraction, Multiplication, Division, etc.) between them is called a linear equation if the highest power of any variable in that equation is one.
    • For example, 5x=15 is a linear equation in one variable i.e., x whereas 2x+3y=5 is a linear equation in two variables x and y.
    For the given problem, we construct a linear equation and solve it to find the answer.
    Let the length of the longer piece of the wire be x m.
    Then, by the question, the other (shorter) piece will be \frac{3}{5}x m long.
    So, the total length will be x+\frac{3}{5} x=\frac{8x}{5} m.
    But according to the question, the total length of the wire is 16 m.
    Thus, we must get \frac{8x}{5}=16. This is the required linear equation to be solved. By solving, we get:
    \frac{8x}{5}=16\\ \Longrightarrow 8x=16\times 5\\\Longrightarrow x=\frac{16\times 5}{8}\\ \therefore x=10
    Also, \frac{3}{5} x=\frac{3}{5}\times 10=6.
    Therefore, the shorter piece of the wire is 6 m long whereas the longer piece is 10 m long.

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