Farmer 5

Farmer Joe ordered three bags of soil last month. Each bag weighed 4 ⅖ kilograms. He used the first bag in a week. At the end of this month, 2 ¾ kilograms of soil were left in the second bag and ⅞ kilograms of soil left in the third bag. How much soil was used this month?

Correct answer:

u =  9 ²³⁄₄₀ = 383/40 kg

Step-by-step explanation:

$$\begin{gathered} n=3 \\ {m}_1=4\frac{2}{5}=4+\frac{2}{5}=\frac{4\cdot 5+2}{5}=\frac{20+2}{5}=\frac{22}{5}=4.4\text{kg} \\ {l}_1=0\text{kg} \\ {l}_2=2\frac{3}{4}=2+\frac{3}{4}=\frac{2\cdot 4+3}{4}=\frac{8+3}{4}=\frac{11}{4}=2.75\text{kg} \\ {l}_3=\frac{7}{8}=0.875\text{kg} \\ m=n\cdot m_1=3\cdot \frac{22}{5}=\frac{3\cdot 22}{5}=\frac{66}{5}=13.2\text{kg} \\ l=l_1+l_2+l_3=0+\frac{11}{4}+\frac{7}{8}=\frac{29}{8}=3.625\text{kg} \\ u=m-l=\frac{66}{5}-\frac{29}{8}=\frac{528}{40}-\frac{145}{40}=\frac{528-145}{40}=\frac{383}{40}=\frac{383}{40}\text{kg}=9\frac{23}{40}\text{kg}=9.575\text{kg} \end{gathered}$$

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