Algebra Warmups
\[ \Large \begin{array} {c c c } & 3 & \color{orange}{X} \\ + & & 7 \\ \hline & 4 & 1 \\ \end{array} \]
What digit in place of \(\color{orange}{X}\) would make the above summation true?
\[ \Large \begin{array} {c c c } & 2 & \color{blue}{A} \\ \times & & 4 \\ \hline & 9 & 6 \\ \end{array} \]
What digit in place of \(\color{blue}{A}\) would make this multiplication true?
\[\Large \begin{array} {c c c } & 1 & \color{blue}{E} \\ \times & & \color{blue}{E} \\ \hline & 9 & \color{blue}{E} \\ \end{array} \]
What digit in place of \(\color{blue}{E}\) would make this multiplication true?
\[ \Large \begin{array} {c c c }
& & \color{green}{C} \\
+ & \color{green}{C} & \color{green}{C} \\
\hline
& \color{purple}{D} & 4 \\
\end{array} \]
In this cryptogram, \(\color{green}{C}\) and \(\color{purple}{D}\) represent two different digits. What is the value of \( \color{green}{C} \)?
\[ \Large \begin{array} { c c c } & 1 & \color{orange}{B} \\ + & \color{orange}{B} & 6 \\ \hline & 7 & 1 \\ \end{array} \]
What digit in place of \(\color{orange}{B}\) would make this sum true?