If a certain recipe takes \( 1 \frac{1}{4} \mathrm{c} \) of sugar and 4 c of water, how much water should be added if the cook only has 1 c of sugar? If the cook only has 1 c of sugar, \( \square \mathrm{c} \) of water should be added. (Simplify your answer. Type an integer, proper fraction, or mixed number.)

To find out how much water should be added if the cook only has 1 c of sugar, we first need to determine the ratio of sugar to water in the original recipe. The recipe calls for \( 1 \frac{1}{4} \) c of sugar, which is equivalent to \( \frac{5}{4} \) c of sugar, and 4 c of water. Next, we calculate the ratio of water to sugar: \[ \frac{4 \text{ c of water}}{\frac{5}{4} \text{ c of sugar}} = \frac{4}{1} \cdot \frac{4}{5} = \frac{16}{5} \text{ c of water for every c of sugar.} \] If the cook only has 1 c of sugar, the amount of water required is: \[ \frac{16}{5} \text{ c of water} = 3 \frac{1}{5} \text{ c of water.} \] So, if the cook only has 1 c of sugar, \( 3 \frac{1}{5} \mathrm{c} \) of water should be added.