Ralph

Ralph has three bulldogs. One weighs 16 1/4 kilos, the other 12 3/5. Suppose the total weight of the three dogs is 45 10/20. What is the weight of the third dog?

Correct answer:

c =  16 ¹³⁄₂₀ = 333/20 kg

Step-by-step explanation:

$$\begin{gathered} a=16\frac{1}{4}=16+\frac{1}{4}=\frac{16\cdot 4+1}{4}=\frac{64+1}{4}=\frac{65}{4}=16.25\text{kg} \\ b=12\frac{3}{5}=12+\frac{3}{5}=\frac{12\cdot 5+3}{5}=\frac{60+3}{5}=\frac{63}{5}=12.6\text{kg} \\ t=45\frac{10}{20}=45+\frac{10}{20}=\frac{45\cdot 20+10}{20}=\frac{900+10}{20}=\frac{910}{20}=\frac{91}{2}=45.5\text{kg} \\ a+b+c=t \\ c=t-a-b=\frac{91}{2}-\frac{65}{4}-\frac{63}{5}=\frac{910}{20}-\frac{325}{20}-\frac{252}{20}=\frac{910-325-252}{20}=\frac{333}{20}=\frac{333}{20}\text{kg}=16\frac{13}{20}\text{kg}=16.65\text{kg} \end{gathered}$$

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