The tub

If we drop the 5 l from the first tap and the second 2 liters of water, the water in the tub will have a temperature of 25 °C. If we drop 3 l from the first tap and from the second 4 l of water, the water in the tub will have a temperature of 21 °C. Determine the water temperatures flowing from both taps.

Final Answer:

a =  29 °C
b =  15 °C

Step-by-step explanation:

$$\begin{gathered} 5a+2b=25\cdot (5+2) \\ 3a+4b=21\cdot (3+4) \\ 5\cdot a+2\cdot b=25\cdot (5+2) \\ 3\cdot a+4\cdot b=21\cdot (3+4) \\ 5a+2b=175 \\ 3a+4b=147 \\ Row2-\frac{3}{5}\cdot Row1\to Row2 \\ 2.8b=42 \\ b=\frac{42}{2.8}=15 \\ a=\frac{175-2b}{5}=\frac{175-2\cdot 15}{5}=29=29\text{°C} \\ a=29 \\ b=15 \end{gathered}$$

Try another example