Question

When making lemonade, you add 1 cup of sugar and 3 cups of lemon juice to half a gallon of water. What is the lemon juice in this mixture?

Answer 1

To find the total volume of the mixture, we first need to convert half a gallon of water into cups. Since there are 16 cups in a gallon, half a gallon is:

\[
\text{Half a gallon} = \frac{16 \text{ cups}}{2} = 8 \text{ cups}
\]

Now we can sum the volumes of all the ingredients used in the lemonade:

- Water: 8 cups
- Sugar: 1 cup
- Lemon juice: 3 cups

Now we add these amounts together to get the total volume of the mixture:

\[
\text{Total volume} = \text{Water} + \text{Sugar} + \text{Lemon juice} = 8 \text{ cups} + 1 \text{ cup} + 3 \text{ cups} = 12 \text{ cups}
\]

To find the proportion of lemon juice in the mixture, we take the amount of lemon juice and divide it by the total volume:

\[
\text{Proportion of lemon juice} = \frac{\text{Lemon juice}}{\text{Total volume}} = \frac{3 \text{ cups}}{12 \text{ cups}} = \frac{1}{4}
\]

Thus, the lemon juice constitutes \(\frac{1}{4}\) of the total mixture.

In conclusion, the answer is:

**3 cups of lemon juice is present in the mixture, which is \(\frac{1}{4}\) of the total mixture.**