Three 109

Three scouts brought three pieces of rope of lengths five and three fourth meters, six and two third meters, and five and five eight meters to their camps. How long are the three pieces together?

Correct answer:

x =  18 ¹⁄₂₄ = 433/24 m

Step-by-step explanation:

$$\begin{gathered} a=5\frac{3}{4}=5+\frac{3}{4}=\frac{5\cdot 4+3}{4}=\frac{20+3}{4}=\frac{23}{4}=5.75\text{m} \\ b=6\frac{2}{3}=6+\frac{2}{3}=\frac{6\cdot 3+2}{3}=\frac{18+2}{3}=\frac{20}{3}\doteq 6.6667\text{m} \\ c=5\frac{5}{8}=5+\frac{5}{8}=\frac{5\cdot 8+5}{8}=\frac{40+5}{8}=\frac{45}{8}=5.625\text{m} \\ x=a+b+c=\frac{23}{4}+\frac{20}{3}+\frac{45}{8}=\frac{138}{24}+\frac{160}{24}+\frac{135}{24}=\frac{138+160+135}{24}=\frac{433}{24}=\frac{433}{24}\text{m}=18\frac{1}{24}\text{m}=18.0417\text{m} \end{gathered}$$

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