2 women share 5 dozen eggs in the ratio 1:2 .
how many eggs does each get.
\(\text{eggs} = 5 * 12 = 60\\ \text{Let } w_1 \text{ first women} \\ \text{Let } w_2 \text{ second women}\)
\(\begin{array}{|lrcll|} \hline (1) & \frac{w_1}{w_2} &=& \frac12 \quad &| \quad \cdot 2\\ & 2\cdot \frac{w_1}{w_2} &=& 1 \quad &| \quad \cdot w_2\\ & 2\cdot w_1 &=& w_2\\ & \mathbf{ w_2 } & \mathbf{=} & \mathbf{2\cdot w_1} \\\\ (2) & w_1+w_2 &=& 60 \text{ eggs} \quad &| \quad w_2 = 2\cdot w_1 \\ & w_1 +2\cdot w_1 &=& 60 \\ & 3\cdot w_1 &=& 60 \quad &| \quad : 3\\ & w_1 &=& \frac{60}{3} \\ & \mathbf{ w_1 } & \mathbf{=} & \mathbf{20 \text{ eggs} } \\\\ & w_2 & = & 60-w_1 \\ & w_2 & = & 60-20 \\ & \mathbf{ w_2 } & \mathbf{=} & \mathbf{40 \text{ eggs} } \\ \hline \end{array} \)
First women get 20 eggs.
Second women get 40 eggs.
check:
20 + 40 = 60
\(\frac{20}{40} = \frac12\)
