Fire victim

Of the 600 3/4 kg of rice donated to the fire victim, 80 1/2 kg came from the learners, and 270 3/4 kg from the teachers. The rest came from the government council. How many kilograms came from the government council?

Correct answer:

c =  249 ¹⁄₂ = 499/2 kg

Step-by-step explanation:

$$\begin{gathered} s=600\frac{3}{4}=600+\frac{3}{4}=\frac{600\cdot 4+3}{4}=\frac{2400+3}{4}=\frac{2403}{4}=600.75\text{kg} \\ a=80\frac{1}{2}=80+\frac{1}{2}=\frac{80\cdot 2+1}{2}=\frac{160+1}{2}=\frac{161}{2}=80.5\text{kg} \\ b=270\frac{3}{4}=270+\frac{3}{4}=\frac{270\cdot 4+3}{4}=\frac{1080+3}{4}=\frac{1083}{4}=270.75\text{kg} \\ a+b+c=s \\ c=s-a-b=\frac{2403}{4}-\frac{161}{2}-\frac{1083}{4}=\frac{2403}{4}-\frac{322}{4}-\frac{1083}{4}=\frac{2403-322-1083}{4}=\frac{998}{4}=\frac{499}{2}\text{kg}=249\frac{1}{2}\text{kg}=249.5\text{kg} \end{gathered}$$

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