# A piano wire is 35" long. A note can be produced by dividing this wire into two parts so that three times the length of the shorter piece is twice the length of the longer piece. What is the length of the shorter piece?

Dec 3, 2016

The shortest length is 14 cm

#### Explanation:

Let the length of the shorter piece be $s$
Let the length of the longer pies be $L$

Then $s + L = 35$

Breaking the question down into its component parts:

..so that three times: " "3xx?
the length of the shorter: $\text{ } 3 \times s$
is :" "3xxs=?
twice the length:" "3xxs=2xx?
of the longer piece:$\text{ } 3 \times s = 2 \times L$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So we have:

$s + L = 35$............................... Equation(1)
$\text{ } 3 s = 2 L$................................Equation(2)

We need to find the value of s so we need to 'get rid' of L

From equation(1) $\text{ "L=35-s" } \ldots \ldots \ldots \ldots . E q u a t i o n \left({1}_{a}\right)$

Using $E q u a t i o n \left({1}_{a}\right)$ substitute for L in $E q u a t i o n \left(2\right)$

$\implies 3 s = 2 L \text{ "->" } 3 s = 2 \left(35 - s\right)$

$3 s = 70 - 2 s$

Add $2 s$ to both sides

$5 s = 70$

Divide both sides by 5

$s = \frac{70}{5} = 14$