Three 109

Three scouts brought three pieces of rope of lengths five and three-fourth meters, six and two-thirds 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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