# Problem of the Day

A teacher buys cookies to divide evenly among the students in her class for a Valentine’s Day party. If of the students are absent, what is the maximum number of cookies she can eat if she wants to be able to feed her class at the rate originally intended?

A. B. C. D. E. [latexpage]

A. $\displaystyle \frac{CP}{K}$

See the Solution

### Solution

[latexpage]

The teacher wants to be able to feed the class at the rate she originally intended. So what is that rate? She bought $C$ cookies to divide among $K$ students, so she wanted to have $\displaystyle \frac{C}{K}$ cookies per student. If this is unclear, plug in some real numbers for $C$ and $K$ and think about what you would do. If she had $60$ cookies for $30$ students, that would obviously be $\displaystyle \frac{60}{30}$ or $2$ cookies per student.

If $P$ of the students are absent, that means she is free to eat their share of the cookies. Their share of the cookies would be $\displaystyle P\cdot \frac{C}{K}$ or Â $\displaystyle \frac{CP}{K}$ cookies. Again, if this is unclear, think about it in terms of real numbers. Â If $10$ of the $30$ students in the example above are absent, she would be free to eat $10\cdot 2=20$ cookies and there would still be enough left to give the remaining students $2$ cookies each.