Salome

Salome bought 4 3/5 kilograms of oranges, 1 kilogram for 2 1/2 GEL (currency Georgian Lari), and 5 1/4 kilograms of apples, 1 kilogram for 1 4/5 GEL. In which fruit did Salome pay more, and by how much?

Correct answer:

x =  21 ¹⁄₁₀ = 211/10 GEL

Step-by-step explanation:

$$\begin{gathered} m_1=4\frac{3}{5}=4+\frac{3}{5}=\frac{4\cdot 5+3}{5}=\frac{20+3}{5}=\frac{23}{5}=4.6\text{kg} \\ {p}_1=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2.5\text{GEL/kg} \\ {m}_2=5\frac{1}{3}=5+\frac{1}{3}=\frac{5\cdot 3+1}{3}=\frac{15+1}{3}=\frac{16}{3}\doteq 5.3333\text{kg} \\ {p}_2=1\frac{4}{5}=1+\frac{4}{5}=\frac{1\cdot 5+4}{5}=\frac{5+4}{5}=\frac{9}{5}=1.8\text{GEL/kg} \\ {c}_1=m_1\cdot p_1=\frac{23}{5}\cdot \frac{5}{2}=\frac{23\cdot 5}{5\cdot 2}=\frac{115}{10}=\frac{23}{2}=11.5\text{GEL} \\ {c}_2=m_2\cdot p_2=\frac{16}{3}\cdot \frac{9}{5}=\frac{16\cdot 9}{3\cdot 5}=\frac{144}{15}=\frac{48}{5}=9.6\text{GEL} \\ x=c_1+c_2=\frac{23}{2}+\frac{48}{5}=\frac{115}{10}+\frac{96}{10}=\frac{115+96}{10}=\frac{211}{10}=\frac{211}{10}\text{GEL}=21\frac{1}{10}\text{GEL}=21.1\text{GEL} \end{gathered}$$

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