Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 68

Evaluate the equation $\displaystyle 0.08x + 0.12(260 - x) = 0.48x$ and check your solution.


$
\begin{equation}
\begin{aligned}

0.08x + 0.12(260 - x) =& 0.48x
&& \text{Given equation}
\\
100 [0.08x + 0.12 (260 - x)] =& 100(0.48x)
&& \text{Multiply each term by $100$}
\\
8x + 12 (260-x) =& 48x
&& \text{Distributive property}
\\
8x + 3120 - 12x =& 48x
&& \text{Distributive property}
\\
-4x + 3120 =& 48x
&& \text{Combine like terms}
\\
-4x - 48x =& -3120
&& \text{Subtract $(48x + 3120)$ from each side}
\\
-52x =& -3120
&& \text{Combine like terms}
\\
\frac{-52x}{-52} =& \frac{-3120}{-52}
&& \text{Divide both sides by $-52$}
\\
x =& 60
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

0.08(60) + 0.12(260 - 60) =& 0.48(60)
&& \text{Let } x = 60
\\
4.8 + 24 =& 28.8
&& \text{Multiply}
\\
28.8 =& 28.8
&& \text{True}

\end{aligned}
\end{equation}
$