Answer: The answer is 4.
Step-by-step explanation: Given that -
The number of cups of yogurt that Carol has to make smoothies is given by
[tex]c_y=1\dfrac{5}{8}=\dfrac{13}{8},[/tex]
and the number of cups of yogurt that each smoothies uses is given by
[tex]c_s=\dfrac{1}{3}.[/tex]
Let 'n' be the number of smoothies that Carol can make with the available yogurt, then we have
[tex]n\times c_s\leq c_y\\\\\\\Rightarrow n\times \dfrac{1}{3}\leq \dfrac{13}{8}\\\\\\\Rightarrow n\leq\dfrac{39}{8}\\\\\\\Rightarrow n\leq 4\dfrac{7}{8}\\\\\\\Rightarrow n=4.[/tex]
Thus, the maximum number of smoothies is 4.
