We have:
Let x = mystery number
Then, the number:
decreased by 7, this is equal to x - 7
then tripled, this is 3(x - 7)
followed by two doublings, this is (2)(2)(3)(x - 7)
resulting in the number 84, this is (2)(2)(3)(x - 7) = 84
Therefore, solve x to find the mystery number:
[tex]\begin{gathered} (2)(2)(3)(x-7)=84 \\ 12(x-7)=84 \\ \frac{12(x-7)}{12}=\frac{84}{12} \\ x-7=7 \\ x-7+7=7+7 \\ x=14 \end{gathered}[/tex]Answer: the mystery number is 14
