Answer: The required number of lemon cookies is 65.
Step-by-step explanation: Given that Stephen is baking cookies for his school bake sale. He bakes 200 cookies.
[tex]\dfrac{1}{2}[/tex] are chocolate chip cookies , [tex]\dfrac{3}{20}[/tex] are peanut butter cookies , [tex]\dfrac{1}{10}[/tex] are sugar cookies and the rest are lemon cookies.
We are to find the number of lemon cookies.
Let n be the required number of lemon cookies.
According to the given information, we have
The number of chocolate chip cookies is
[tex]n_c=\dfrac{1}{2}\times200=100,[/tex]
the number of peanut butter cookies is
[tex]n_p=\dfrac{3}{20}\times100=15[/tex]
and the number of sugar cookies is
[tex]n_s=\dfrac{1}{10}\times200=20.[/tex]
Therefore, we must have
[tex]100+15+20+n=200\\\\\Rightarrow 135+n=200\\\\\Rightarrow n=200-135\\\\\Rightarrow n=65.[/tex]
Thus, the required number of lemon cookies is 65.
