Question

Use your proportion to write an equation for the number of cups of sugar based on the number of cups of lemonade
1 cup sugar
1 cup water
1 cup lemon juice
4 cups of cold water

Answer 1

To create an equation for the number of cups of sugar based on the number of cups of lemonade, we first need to identify the total volume of the lemonade based on the ingredients you've provided.

From your recipe, we have:

- 1 cup sugar
- 1 cup water
- 1 cup lemon juice
- 4 cups cold water

Now, let's calculate the total volume of the lemonade:

Total volume = 1 cup sugar + 1 cup water + 1 cup lemon juice + 4 cups cold water
Total volume = 1 + 1 + 1 + 4
Total volume = 7 cups of lemonade

In this mixture, the ratio of sugar to total lemonade is:

\[
\text{Ratio of sugar to lemonade} = \frac{\text{cups of sugar}}{\text{total cups of lemonade}} = \frac{1}{7}
\]

Now, if we let \( L \) represent the number of cups of lemonade, we can express the number of cups of sugar \( S \) as follows:

Since 1 cup of sugar corresponds to 7 cups of lemonade, the equation becomes:

\[
S = \frac{1}{7} L
\]

This equation means that for every cup of lemonade, you need \(\frac{1}{7}\) of a cup of sugar.