Originally Posted by

**CaptainBlack** Let the amount of coffee consumed by the class be $\displaystyle c$ cups

Let the amout of milk consumed by the class be $\displaystyle m$ cups.

We do not assume that $\displaystyle c$ and/or $\displaystyle m$ are integers,

just that they are greater or equal to zero.

Kathy drank a cup of coffee milk mixture, and from what we are told we

know that:

$\displaystyle

1=\frac{c}{5}+\frac{m}{7}

$.

Rearranging this gives:

$\displaystyle

35=7c+5m\ \ \ \dots(1)

$.

Also if there are $\displaystyle N$ students in the class, as they each drink a cup we have:

$\displaystyle

N=c+m\ \ \ \dots(2)

$.

From $\displaystyle (1)$ it is clear that $\displaystyle c\le 5$ cups and $\displaystyle m \le 7$, so $\displaystyle N \le 12$