A faulty Celsius thermometer reads 0.7°C at the melting point of pure ice and 99.5°C at the boiling point of water at normal pressure. At what temp. will its reading be exactly correct?

Please explain in detail cause i don't rly understand the question " At what temp. will its reading be exactly correct?" in itself.

At [tex]\displaystyle\bf58\frac{1}{3}^o[/tex], the faulty Celsius thermometer will have the correct reading. (which means the standard Celsius thermometer also have the same reading)

Explanation:

We can find the temperature which both the faulty and standard Celsius thermometers have the same reading by matching their:

melting points
boiling points
scale

Let the faulty Celsius thermometer's readings in °X, whereas the standard Celsius thermometer's readings in °C

Given:

melting points: 0°C = 0.7°X
boiling points: 100°C = 99.5°X
scale: (100 - 0)°C = (99.5 - 0.7)°X

100°C = 98.8°X

1°C = 0.988°X

Let the same reading is n°C. Then, the reading at the faulty thermometer is also n°X

To convert n°C into °X:

[tex]\boxed{n^oC = (0.988n + 0.7)^oX}[/tex]

[tex]n^oC=n^oX[/tex]

[tex](0.988n + 0.7)^oX=n^oX[/tex]

[tex]n-0.988n=0.7[/tex]

[tex]n=0.7\div0.012[/tex]

[tex]\displaystyle=58\frac{1}{3}[/tex]