Apple purchase

Three classmates bought apples. Peter bought two whole one-thirds of the kg, Spring 5 sixths of a kg less than Peter and Daniel 2 times as much as Peter. How many kilograms of apples did the boys buy together?

Final Answer:

x =  8 ¹⁄₂ = 17/2 kg

Step-by-step explanation:

$$\begin{gathered} P=2\frac{1}{3}=2+\frac{1}{3}=\frac{2\cdot 3+1}{3}=\frac{6+1}{3}=\frac{7}{3}\doteq 2.3333\text{kg} \\ J=P-\frac{5}{6}=\frac{7}{3}-\frac{5}{6}=\frac{14}{6}-\frac{5}{6}=\frac{14-5}{6}=\frac{9}{6}=\frac{3}{2}=1.5\text{kg} \\ D=2\cdot P=2\cdot \frac{7}{3}=\frac{2\cdot 7}{3}=\frac{14}{3}\doteq 4.6667\text{kg} \\ x=P+J+D=\frac{7}{3}+\frac{3}{2}+\frac{14}{3}=\frac{14}{6}+\frac{9}{6}+\frac{28}{6}=\frac{14+9+28}{6}=\frac{51}{6}=\frac{17}{2}\text{kg}=8\frac{1}{2}\text{kg}=8.5\text{kg} \end{gathered}$$

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