Suppose you have designed a new thermometer called the X thermometer. On the X scale the boiling point of water is 130 °X and the freezing point of water is 10 °X. At what temperature will the readings on the Fahrenheit and X thermometers be the same?

Originally, I thought I knew exactly how to solve this problem. I thought just knowing that the freezing point of water is 32*F and the boiling point of water is 212*F would easily help me solve this, but I’m quite stuck. Conversions from F to C or vice versa have an easy equation to follow, but I’m not exactly sure what my first step should be here. Does anyone know what the first step would be? Here is what I have so far.

130*X = 212*F

10*X = 32*F

The difference between the freezing point and boiling point in X is 120. The difference between the freezing point and boiling point in F is 180.