Mrs. Dinah

Mrs. Dinah Tah Tanda divided her lot among her 4 children. The first got 3 1/2 ha, the second 3 1/3 ha, the third 3 1/4 ha, and the fourth 3 2/5 ha. How big is Mrs. Tanda's lot?

Final Answer:

x =  13 ²⁹⁄₆₀ = 809/60 ha

Step-by-step explanation:

$$\begin{gathered} a=3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{6+1}{2}=\frac{7}{2}=3.5\text{ha} \\ b=3\frac{1}{3}=3+\frac{1}{3}=\frac{3\cdot 3+1}{3}=\frac{9+1}{3}=\frac{10}{3}\doteq 3.3333\text{ha} \\ c=3\frac{1}{4}=3+\frac{1}{4}=\frac{3\cdot 4+1}{4}=\frac{12+1}{4}=\frac{13}{4}=3.25\text{ha} \\ d=3\frac{2}{5}=3+\frac{2}{5}=\frac{3\cdot 5+2}{5}=\frac{15+2}{5}=\frac{17}{5}=3.4\text{ha} \\ x=a+b+c+d=\frac{7}{2}+\frac{10}{3}+\frac{13}{4}+\frac{17}{5}=\frac{210}{60}+\frac{200}{60}+\frac{195}{60}+\frac{204}{60}=\frac{210+200+195+204}{60}=\frac{809}{60}=\frac{809}{60}\text{ha}=13\frac{29}{60}\text{ha}=13.4833\text{ha} \end{gathered}$$

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