Given:
A recipe calls for a total of 3 and two-thirds cups flour and sugar respectively.
To find:
The flour needed if the recipe calls for one-fourth cup of sugar.
Solution:
According to the question,
[tex]\dfrac{2}{3}[/tex] of sugar needs 3 cups of flour.
[tex]1[/tex] of sugar needs [tex]\dfrac{3}{2}\times 3[/tex] cups of flour.
[tex]\dfrac{1}{4}[/tex] of sugar needs [tex]\dfrac{1}{4}\times \dfrac{3}{2}\times 3[/tex] cups of flour.
Now,
[tex]\text{Required flour}=\dfrac{1}{4}\times \dfrac{3}{2}\times 3[/tex]
[tex]\text{Required flour}=\dfrac{9}{8}[/tex]
Therefore, the required flour is [tex]\dfrac{9}{8}[/tex] cups.
