Final answer:
The lower and upper bounds of the temperature at noon in Madrid are 24.36 C and 26.44 C, after considering the precise recording in Liverpool and the rounded differences in temperatures when compared to Budapest and Madrid.
Step-by-step explanation:
To find the lower and upper bounds for the temperature in Madrid, we start by determining the temperature in Budapest, which is “16 degrees C colder than Liverpool”, and then calculate the bounds for Madrid which is “24 degrees C warmer than the temperature in Budapest”.
The temperature in Liverpool is 17.4 degrees C, measured to the nearest 0.1 degrees C, so its lower bound is 17.35 C and its upper bound is 17.45 C. The temperature in Budapest, measured to the nearest degree, is 16 degrees C cooler. The largest the difference could be while still rounding to 16 C is 16.49 C cooler, and the smallest difference could be 15.5 C cooler. This gives us bounds for Budapest's temperature:
- Upper Bound: 17.45 - 15.5 = 1.95 C
- Lower Bound: 17.35 - 16.49 = 0.86 C
For Madrid, which is 24 degrees C warmer than Budapest to the nearest degree, we'd have a maximum possible difference of 24.49 C and a minimum of 23.5 C.
- Madrid Upper Bound: 1.95 + 24.49 = 26.44 C
- Madrid Lower Bound: 0.86 + 23.5 = 24.36 C
The lower and upper bounds of the temperature at noon in Madrid are 24.36 C and 26.44 C respectively.