Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 64

Evaluate the equation $\displaystyle 0.09x + 0.13 (x + 300) = 61$ and check your solution.


$
\begin{equation}
\begin{aligned}

0.09x + 0.13 (x + 300) =& 61
&& \text{Given equation}
\\
100 [0.09x + 0.13(x + 300)] =& 61(100)
&& \text{Multiply each term by $100$}
\\
9x + 13(x +300) =& 6100
&& \text{Distributive property}
\\
9x + 13x + 3900 =& 6100
&& \text{Distributive property}
\\
22x + 3900 =& 6100
&& \text{Combine like terms}
\\
22x =& 6100 - 3900
&& \text{Subtract $3900$ from each side}
\\
22x =& 2200
&& \text{Combine like terms}
\\
\frac{22x}{22} =& \frac{2200}{22}
&& \text{Divide both sides by $22$}
\\
x =& 100
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

0.09(100) + 0.13(100 + 300) =& 61
&& \text{Let } x = 100
\\
9 + 52 =& 61
&& \text{Multiply}
\\
61 =& 61
&& \text{True}

\end{aligned}
\end{equation}
$