Respuesta :
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
After constructing and solving the linear equation [tex]x+\frac{3}{5}x=16[/tex], we obtain that the shorter piece of the wire is [tex]6[/tex] m long whereas the longer piece is [tex]10[/tex] 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, [tex]5x=15[/tex] is a linear equation in one variable i.e., [tex]x[/tex] whereas [tex]2x+3y=5[/tex] is a linear equation in two variables [tex]x[/tex] and [tex]y[/tex].
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 [tex]x[/tex] m.
Then, by the question, the other (shorter) piece will be [tex]\frac{3}{5}x[/tex] m long.
So, the total length will be [tex]x+\frac{3}{5} x=\frac{8x}{5}[/tex] m.
But according to the question, the total length of the wire is [tex]16[/tex] m.
Thus, we must get [tex]\frac{8x}{5}=16[/tex]. This is the required linear equation to be solved. By solving, we get:
[tex]\frac{8x}{5}=16\\ \Longrightarrow 8x=16\times 5\\\Longrightarrow x=\frac{16\times 5}{8}\\ \therefore x=10[/tex]
Also, [tex]\frac{3}{5} x=\frac{3}{5}\times 10=6[/tex].
Therefore, the shorter piece of the wire is [tex]6[/tex] m long whereas the longer piece is [tex]10[/tex] m long.
