Answer: The correct option is (B). [tex]\dfrac{2}{7}<\dfrac{3}{1}.[/tex]
The ratio of sugar to flour is [tex]\dfrac{2}{7}[/tex] and the ratio of milk to oil is [tex]\dfrac{3}{1}.[/tex]
Step-by-step explanation: Given that a cake mix calls for the following ingredients:
2 cups of sugar , 7 cups of flour , 3 cups of milk and 1 cup of oil.
We are given to write the ratios of sugar to flour and milk to oil and select the correct comparison of the ratios.
The ratio of sugar to flour is given by
[tex]R_{sf}=\dfrac{\textup{quantity of sugar}}{\textup{quantity of flour}}\\\\\\\Rightarrow R_{sf}=\dfrac{2}{7},[/tex]
and the ratio of milk to oil is given by
[tex]R_{mo}=\dfrac{\textup{quantity of milk}}{\textup{quantity of oil}}\\\\\\\Rightarrow R_{mo}=\dfrac{3}{1}.[/tex]
Since
[tex]\dfrac{3}{1}=\dfrac{3\times7}{1\times7}=\dfrac{21}{7},[/tex]
so have
[tex]\dfrac{2}{7}<\dfrac{21}{7}\\\\\\\Rightarrow \dfrac{2}{7}<\dfrac{3}{1}.[/tex]
Thus, the ratio of sugar to flour is [tex]\dfrac{2}{7}[/tex] and the ratio of milk to oil is [tex]\dfrac{3}{1}.[/tex] The correct comparison is [tex]\dfrac{2}{7}<\dfrac{3}{1}.[/tex]
Option (B) is CORRECT.
