Dukáty

Štyria chlapci odovzdali papier do zberu. Ján dostal 111 1/3 dukáta, Michal 228 3/4, Peter 195 1/2 dukáta a Róbert 146 1/4 dukáta. Koľko kg papiera priniesol každý chlapec, ak papier vykupovali po 2,50 dukáta za kg?

Správna odpoveď:

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

Postup správneho riešenia:

$$\begin{gathered} c=2,5\text{d/kg} \\ {d}_1=111\frac{1}{3}=111+\frac{1}{3}=\frac{111\cdot 3+1}{3}=\frac{333+1}{3}=\frac{334}{3}\doteq 111,3333 \\ J=d_1/c=111,3333/2,5=\frac{668}{15}\text{kg}=44\frac{8}{15}\text{kg}=44,5333\text{kg} \end{gathered}$$

$$\begin{gathered} d_2=228\frac{3}{4}=228+\frac{3}{4}=\frac{228\cdot 4+3}{4}=\frac{912+3}{4}=\frac{915}{4}=228,75 \\ M=d_2/c=228,75/2,5=\frac{183}{2}\text{kg}=91\frac{1}{2}\text{kg}=91,5\text{kg} \end{gathered}$$

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

$$\begin{gathered} d_4=146\frac{1}{4}=146+\frac{1}{4}=\frac{146\cdot 4+1}{4}=\frac{584+1}{4}=\frac{585}{4}=146,25 \\ R=d_4/c=146,25/2,5=\frac{117}{2}\text{kg}=58\frac{1}{2}\text{kg}=58,5\text{kg} \end{gathered}$$

Skúsiť iný príklad