Answer
\[\underline{34{}^\circ \text{F}}\]
Work Step by Step
The boiling point of water is \[130{}^\circ \text{X}\].
The freezing point of water is \[10{}^\circ \text{X}\].
The boiling point of water on the Fahrenheit scale is \[\text{212}{}^\circ \text{F}\].
The freezing point of water on the Fahrenheit scale is \[\text{32}{}^\circ \text{F}\].
\[\begin{align}
& \frac{\left( F-32 \right)}{\left( 212-32 \right)}=\frac{\left( X-10 \right)}{\left( 130-10 \right)} \\
& \frac{\left( F-32 \right)}{180}=\frac{\left( X-10 \right)}{120} \\
& 1.5X+17=F
\end{align}\]
When the reading on the Fahrenheit scale will be the same as that of the X scale, the above equation will become
\[\begin{align}
& 1.5X+17=X \\
& X=34{}^\circ
\end{align}\]
The temperature at which the Fahrenheit and X readings are the same is \[\underline{34{}^\circ \text{F}}\].
