Paper harvest

Four boys passed the paper to harvest. John received 111 1/3 ducats, Michael 228 3/4, Peter 195 1/2 ducats, and Robert 146 1/4 ducats. How many kg of paper did each boy bring if they bought paper at 2.50 ducats per kg?

Final Answer:

J =  44 ⁸⁄₁₅ = 668/15 kg
M =  91 ¹⁄₂ = 183/2 kg
P =  78 ¹⁄₅ = 391/5 kg
R =  58 ¹⁄₂ = 117/2 kg

Step-by-step explanation:

$$\begin{gathered} c=2.5\text{d/kg} \\ {d}_1=111\frac{1}{3}=111+\frac{1}{3}=\frac{111\cdot 3+1}{3}=\frac{333+1}{3}=\frac{334}{3}\doteq 111.3333 \\ J=d_1/c=111.3333/2.5=\frac{668}{15}\text{kg}=44\frac{8}{15}\text{kg}=44.5333\text{kg} \end{gathered}$$

$$\begin{gathered} d_2=228\frac{3}{4}=228+\frac{3}{4}=\frac{228\cdot 4+3}{4}=\frac{912+3}{4}=\frac{915}{4}=228.75 \\ M=d_2/c=228.75/2.5=\frac{183}{2}\text{kg}=91\frac{1}{2}\text{kg}=91.5\text{kg} \end{gathered}$$

$$\begin{gathered} d_3=195\frac{1}{2}=195+\frac{1}{2}=\frac{195\cdot 2+1}{2}=\frac{390+1}{2}=\frac{391}{2}=195.5 \\ P=d_3/c=195.5/2.5=\frac{391}{5}\text{kg}=78\frac{1}{5}\text{kg}=78.2\text{kg} \end{gathered}$$

$$\begin{gathered} d_4=146\frac{1}{4}=146+\frac{1}{4}=\frac{146\cdot 4+1}{4}=\frac{584+1}{4}=\frac{585}{4}=146.25 \\ R=d_4/c=146.25/2.5=\frac{117}{2}\text{kg}=58\frac{1}{2}\text{kg}=58.5\text{kg} \end{gathered}$$

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