Castle Museum

Many medieval cannons made of cannon were found in the Castle Museum (cannon is an alloy of tin and copper in a ratio of 1:9). The councilors agreed that they did not need cannons, but a new bell would be thrown at the town tower. The bells are made of bells, which are also an alloy of tin and copper, but in a ratio of 1:4. Calculate how much cannon and how much tin will be needed to produce a 500 kg bell made of bells.

Correct answer:

d =  444.4444 kg
s =  55.5556 kg

Step-by-step explanation:

$$\begin{gathered} m=500\text{kg} \\ CU=\frac{4}{1+4}\cdot m=\frac{4}{1+4}\cdot 500=400\text{kg} \\ CU=\frac{9}{1+9}\cdot d \\ d=\frac{10}{9}\cdot CU=\frac{10}{9}\cdot 400=\frac{10\cdot 400}{9}=\frac{4000}{9}=\frac{4000}{9}\text{kg}=444.4444\text{kg} \end{gathered}$$

$$\begin{gathered} s=m-d=500-\frac{4000}{9}=\frac{500\cdot 9}{9}-\frac{4000}{9}=\frac{4500}{9}-\frac{4000}{9}=\frac{4500-4000}{9}=\frac{500}{9}\doteq 55.5556\text{kg} \\ \text{ Verifying Solution: } \\ {s}_1=\frac{1}{1+9}\cdot d=\frac{1}{1+9}\cdot \frac{4000}{9}=\frac{400}{9}\doteq 44.4444\text{kg} \\ {p}_1=s_1:CU=\frac{400}{9}:400=\frac{400}{9\cdot 400}=\frac{400}{3600}=\frac{1}{9}\doteq 0.1111=1:9 \\ {p}_2=(s_1+s):CU=(\frac{400}{9}+\frac{500}{9}):400=\frac{1}{4}=0.25=1:4 \end{gathered}$$

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