Intermediate Algebra, Chapter 2, 2.3, Section 2.3, Problem 20

Use the variable $x$ for the unknown, and write an equation representing the verbal sentence "when $75 \% $ of a number is added to $6$, the result is $3$ more than the number". Find the number and solve the problem.

The equation is


$
\begin{equation}
\begin{aligned}

0.75x + 6 =& x + 3
&& \text{Write $75 \%$ as decimal}
\\
0.75x - x =& 3 - 6
&& \text{Subtract each side by $(x + 6)$}
\\
-0.25x =& -3
&& \text{Combine like terms}
\\
x =& 12
&& \text{Divide each side by $-0.25$}

\end{aligned}
\end{equation}
$