Mary is baking a cake. The recipe calls for 11 cups of sugar and 9 cups of flour. She already put in 12 cups of flour and 10 cups of sugar. How many more cups of sugar does she need to add?
We have:
$$
s = 11, \; f = 9, \; S = 12, \; F = 10
$$

We need to find:
$$
S - s = ?
$$

We know that:
$$
S + f = F, \; s + F = S
$$

Therefore:
$$
S - s = F - f = 10 - 9 = 1
$$

So, Mary needs to add 1 more cup of sugar.