Question

Find the value of the variable.

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

Short answer

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

Step-by-step solution

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

role="math" localid="1638271233655">3180−y=290−y3×180−3×y=2×90−2×y540−3y=180−2y

Step 2. Add 3y.

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

role="math" localid="1638271418146" $\begin{array}{l}540-3y+3y=180-2y+3y\\ 540=180+y\end{array}$

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

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

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