https://file.aiquickdraw.com/mathbot/file/1726791448995d66dgoby.jpg

https://file.aiquickdraw.com/mathbot/file/1726791448996bemuiu1d.jpg

can u give me an explanation for this, no answer pls 

To explain the problem:

### Scenario:
Deondra has **$12** to spend on a combination of **green grapes** and **red grapes**. 
- **Green grapes** cost **$3 per pound**.
- **Red grapes** cost **$2 per pound**.

### Goal:
We need to create an equation that represents the total amount of grapes she can buy, within her $12 budget. The equation should involve two variables, where:
- Let **g** represent the number of pounds of green grapes she buys.
- Let **r** represent the number of pounds of red grapes she buys.

### Setting up the Equation:
The total cost of the green grapes would be **3g** (because each pound of green grapes costs $3, and she buys g pounds).
The total cost of the red grapes would be **2r** (because each pound of red grapes costs $2, and she buys r pounds).

Since her total budget is $12, the equation balancing the cost of both types of grapes must equal 12:

\[
3g + 2r = 12
\]

### Meaning of the Equation:
This equation can be used to graph the different combinations of green and red grapes that Deondra can buy, as long as the total cost does not exceed $12.

Let me know if you'd like further details on how to graph this or solve for specific values!

---

### Relative Questions:
1. How do you graph the equation $3g + 2r = 12$?
2. What are some possible combinations of green and red grapes Deondra can buy with $12?
3. How would the equation change if the prices of the grapes were different?
4. Can Deondra buy only one type of grape, and if so, how many pounds?
5. How would you interpret the slope of the line in the graph of this equation?

### Tip:
When setting up equations for a budget, always ensure that the total cost for all items equals the available budget!

Deondra has $12 to spend on a mixture of green and red grapes. What equation can she use to graph a line showing the different amounts of green and red grapes she can buy for $12?

Learn how to create a linear equation that represents the budget constraints when buying green and red grapes. The problem involves graphing the equation 3g + 2r = 12 to visualize how many pounds of grapes can be bought within a $12 budget. Suitable for Grades 6-8.

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