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.

Answer 1

After constructing and solving the linear equation
`x+(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
`(3)/(5)x` m long.

So, the total length will be
`x+(3)/(5) x=(8x)/(5)` m.

But according to the question, the total length of the wire is
`16` m.

Thus, we must get
`(8x)/(5)=16`. This is the required linear equation to be solved. By solving, we get:

`(8x)/(5)=16\\ \Longrightarrow 8x=16* 5\\\Longrightarrow x=(16* 5)/(8)\\ \therefore x=10`

Also,
`(3)/(5) x=(3)/(5)* 10=6`.

Therefore, the shorter piece of the wire is
`6` m long whereas the longer piece is
`10` m long.

Answer 2

The longer piece is 10 m, and the shorter piece is 6 m.

Explanation:

16 / (5 + 3) = 2 m

2 x 5 = 10 m

2 x 3 = 6 m