In a field, the grass increases in a constant rate. $17$ cows can eat all the grass in the field in $30$ days. $19$ cows can eat all the grass in $24$ days. Suppose, a group of cows started eating grass for $6$ days. Then $4$ cows are sold. The rest cows took $2$ more days to eat the remaining grass. What is the number of cows in the group?

## My trying:

A cow eats a certain amount of grass in one day, call it $c$. The field grows by a certain amount each day, call it $g$.

The field has some initial amount of grass: $i$

\begin{equation} \begin{aligned} i + 30g - 17\cdot30c &= 0\\ i+24g-19\cdot24c&=0 \end{aligned} \end{equation}

Solving these two equations we get , $g = 9c$ . That means It takes 9 cows to eat one day's growth in one day.