That's great to hear! A linear relationship between the number of glasses sold and total profits means that for every additional glass of lemonade Rebecca sells, she makes a consistent amount of money.
Let's say Rebecca sells each glass of lemonade for a certain price, and she incurs a fixed cost per glass (or no cost if she doesn't have any expenses). The total profit she makes can be expressed with the following linear equation:
\[ \text{Total Profit} = (\text{Price per Glass} \times \text{Number of Glasses Sold}) - \text{Fixed Costs} \]
If we want to illustrate this further, we can use variables:
- Let \( P \) be the price per glass of lemonade.
- Let \( N \) be the number of glasses sold.
- Let \( C \) be the total fixed costs (if any).
Then, the equation for her total profit \( T \) would look like this:
\[ T = P \times N - C \]
If the fixed costs are zero, then the relationship simplifies to:
\[ T = P \times N \]
This means that for every glass sold, Rebecca's total profit increases by the price of each glass, reflecting a direct linear relationship.
Since she plans to donate her profits to the local animal shelter, the more lemonade she sells, the more funds she can generate for the shelter. This can also encourage her to sell more glasses in a community effort to support a good cause!
If you have specific numbers for price, number of glasses, or fixed costs, we could calculate her total profit!
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