Exercise 41
If 17 is added to a number, then 5 is subtracted from the sum, and the resulting difference is multiplied by 4, the result is 132. What was the original number?
-
10
-
12
-
19
-
21
-
31
Try to solve it before checking the answer.
-
21
If \(x\) is the original number, we have:
\[
\begin{aligned}
&4 \left[ (x + 17) – 5 \right] = 132
\\[.5em]
&\hspace{5em}\Rightarrow
4 (x + 17) – 20 = 132
\\[.5em]
&\hspace{5em}\Rightarrow
4x + 68 – 20 = 132
\\[.5em]
&\hspace{5em}\Rightarrow
4x = 84
\\[.5em]
&\hspace{5em}\Rightarrow
\boldsymbol{
x = 21
}
\end{aligned}
\]
\[
\begin{aligned}
4 \left[ (x + 17) – 5 \right] = 132
&\Rightarrow
4 (x + 17) – 20 = 132
\\[.5em]
&\Rightarrow
4x + 68 – 20 = 132
\\[.5em]
&\Rightarrow
4x = 84
\\[.5em]
&\Rightarrow
\boldsymbol{
x = 21
}
\end{aligned}
\]