Q46 - Geometry

Question

Find the value of the variable.

$3\left(180-y\right)=2\left(90-y\right)$

Step-by-Step Solution

Answer

The value of the variable is $\mathit{y}\mathbf{=}\mathbf{360}$.

Step 1. Apply the distributive property of multiplication.

The formula of distributive property of multiplication is given by: $x\left(y+z\right)=xy+xz$. Apply this property to the equation $3\left(180-y\right)=2\left(90-y\right)$.

style="width:30%" width="215" height="72" style="max-width: none; vertical-align: -31px;" $\begin{array}{l} 3\left(180-y\right)=2\left(90-y\right)\\ 3\times 180-3\times y=2\times 90-2\times y\\ 540-3y=180-2y\end{array}$

Step 2. Add 3 y .

To further simplify, add 3y from both sides of the equation $540-3y=180-2y$.

$\begin{array}{l}540-3y+3y=180-2y+3y\\ 540=180+y\end{array}$ 

Step 3. Subtract 180.

To find the value of variable y in the equation $540=180+y$, subtract 180 from both sides of the equation.

$\begin{array}{l}540-180=180+y-180\\ 360=y\end{array}$

Step 4. Verify the value.

In order to verify the value of y, substitute 360 for y into the equation $3\left(180-y\right)=2\left(90-y\right)$.

$\begin{array}{l}3\left(180-360\right)=2\left(90-360\right)\\ 3\left(-180\right)=2\left(-270\right)\\ -\text{540}=-\text{540 True}\end{array}$

Hence, the value of the variable is $y=360$.