A thermometer graduated according to a linear scale reads a value x₀ when in contact with boiling water, and x₀/3 when in contact with ice. What is the temperature of an object in °C, if this thermometer in contact with the object reads x₀/2?

Let T be the temperature in °C.
Let x be the reading on the thermometer.
When the thermometer is in contact with boiling water (100°C), the reading is x₀.
When the thermometer is in contact with ice (0°C), the reading is x₀/3.
We can assume a linear relationship between the temperature and the thermometer reading:
T = m x + c
where m is the slope and c is the y-intercept.
Using the two points (100, x₀) and (0, x₀/3), we can find m and c:
100 = m x₀ + c
0 = m (x₀/3) + c
Subtracting the second equation from the first:
100 = m x₀ - m (x₀/3)
100 = (2/3) m x₀
m = 150/x₀
Substituting m into the second equation:
0 = (150/x₀) (x₀/3) + c
c = -50
So the equation is:
T = (150/x₀) x - 50
If the thermometer reads x₀/2, then:
T = (150/x₀) (x₀/2) - 50
T = 75 - 50
T = 25°C