https://file.aiquickdraw.com/mathbot/file/1726670646685psoclnet.jpg

Let's analyze the problem and the possible equations from the image:

### Given Information:
1. **Milk**: Jada prepares 12 ounces of milk per person. A 1-gallon jug contains 128 ounces and costs $3.
2. **Cookies**: Jada prepares 4 cookies per person. A package of 24 cookies costs $4.50.
3. **People**: Including herself, there are 15 people in total.
4. **Variables**:
   - $ n $: Number of people in the club (15 people).
   - $ m $: Ounces of milk Jada needs.
   - $ c $: Number of cookies Jada needs.
   - $ b $: Jada’s total budget.

### Equations Setup:
1. **Milk Consumption**: Jada prepares 12 ounces of milk per person.
   - $ m = 12n $ → Since $ n = 15 $, this becomes $ m = 12(15) = 180 $ ounces of milk.
   
2. **Cookie Consumption**: Jada prepares 4 cookies per person.
   - $ c = 4n $ → Since $ n = 15 $, this becomes $ c = 4(15) = 60 $ cookies.
   
3. **Number of Cookie Packages**: Each package contains 24 cookies.
   - Number of packages = $ \frac{c}{24} = \frac{60}{24} = 2.5 $ packages.
   
4. **Milk Cost**: The milk comes in 1-gallon jugs (128 ounces per gallon).
   - Jada needs 180 ounces, so the number of gallons is $ \frac{180}{128} \approx 1.40625 $ gallons.
   - Total milk cost = $ 1.40625 \times 3 \approx 4.22 $ dollars.
   
5. **Cookies Cost**: Each package of cookies costs $4.50.
   - Total cookies cost = $ 2.5 \times 4.50 = 11.25 $ dollars.

6. **Total Budget (b)**: 
   - Total budget $ b $ = Milk cost + Cookies cost = $ 4.22 + 11.25 = 15.47 $ dollars.

### Equations to Check:
Now let's look at the equations provided in the image and analyze which ones are correct based on the setup.

1. **$ 3m + 4.5c = b $**: 
   - This equation is incorrect. The variables $ m $ and $ c $ represent the quantities of milk and cookies, not their costs. The equation mixes quantities and dollars.

2. **$ b = 2(3) + 3(4.50) $**:
   - This seems incorrect because it implies some multiplication involving the cost of milk and cookies, but the math doesn’t align with the correct total cost.

3. **$ 4(4.50) = c $**:
   - This equation is incorrect. It suggests that multiplying 4 by the cost of a cookie package gives the total number of cookies, which is wrong.

4. **$ m = 12(15) $**:
   - This equation is **correct** as it represents the total amount of milk (180 ounces) for 15 people at 12 ounces per person.

5. **$ n = 12(15) $**:
   - This is incorrect because $ n $ represents the number of people, and $ n = 15 $ already.

### Correct Answer(s):
- The correct equation that represents the quantities and constraints is **$ m = 12(15) $**. 

Would you like to explore these concepts in further detail?

Here are some related questions for practice:
1. How much would Jada's budget be if the price of a gallon of milk increased by 10%?
2. If Jada wanted to prepare 5 cookies per person instead of 4, how many packages of cookies would she need?
3. How many gallons of milk would Jada need if there were 20 people in the club?
4. What would happen to Jada's total budget if the price of a cookie package decreased by 20%?
5. If the price of cookies remains constant but Jada wants to prepare for 18 people, what is her total cost for milk and cookies?

**Tip**: Always separate the variables representing quantities from those representing costs to avoid confusion when setting up equations.

Jada plans to serve milk and healthy cookies for a book club meeting. She is preparing 12 ounces of milk and 4 cookies per person. Including herself, there are 15 people in the club. A package of cookies contains 24 cookies and costs $4.50. A 1-gallon jug of milk contains 128 ounces and costs $3. Let n represent the number of people in the club, m represent the ounces of milk, c represent the number of cookies, and b represent Jada's budget in dollars. Select all the equations that could represent the quantities and constraints in this situation.

Learn how to set up and solve linear equations involving quantities of milk and cookies for a group of 15 people. Explore how unit conversions and cost calculations affect the overall budget using algebraic equations.

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