A pack 2

A pack of all-purpose flour weighs 4 1/4 kilograms. Grace uses 1 1/2 packs of flour for baking a cake and 1 2/3 bags of flour for bread. How many kilograms did she use?

Correct answer:

m =  13 ¹¹⁄₂₄ = 323/24 kg

Step-by-step explanation:

$$\begin{gathered} m_1=4\frac{1}{4}=4+\frac{1}{4}=\frac{4\cdot 4+1}{4}=\frac{16+1}{4}=\frac{17}{4}=4.25\text{kg} \\ {p}_1=1\frac{1}{2}=1+\frac{1}{2}=\frac{1\cdot 2+1}{2}=\frac{2+1}{2}=\frac{3}{2}=1.5 \\ {p}_2=1\frac{2}{3}=1+\frac{2}{3}=\frac{1\cdot 3+2}{3}=\frac{3+2}{3}=\frac{5}{3}\doteq 1.6667 \\ p=p_1+p_2=\frac{3}{2}+\frac{5}{3}=\frac{9}{6}+\frac{10}{6}=\frac{9+10}{6}=\frac{19}{6}\doteq 3.1667 \\ m=m_1\cdot p=\frac{17}{4}\cdot \frac{19}{6}=\frac{17\cdot 19}{4\cdot 6}=\frac{323}{24}=\frac{323}{24}\text{kg}=13\frac{11}{24}\text{kg}=13.4583\text{kg} \end{gathered}$$

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