Mr. Hernandez combines 1 gallon of orange juice, 3 pints of pineapple juice, and 2 quarts of lemon lime soda to make punch for a party. He allows 2 cups of punch for each guest. How many guests can he serve? How much punch will be left?

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UpStudy AI · Accepted Answer

To solve the problem, we need to first convert all the liquid measurements to the same unit, which will make it easier to calculate the total volume of punch Mr. Hernandez has prepared.

### Step 1: Convert all measurements to cups
1. **Orange Juice**: 
   - 1 gallon = 16 cups (since 1 gallon = 4 quarts and 1 quart = 4 cups)
   
2. **Pineapple Juice**: 
   - 3 pints = 6 cups (since 1 pint = 2 cups)
   
3. **Lemon Lime Soda**: 
   - 2 quarts = 8 cups (since 1 quart = 4 cups)

### Step 2: Calculate the total volume of punch
Now, we can add all the cups together:
$$
\text{Total Punch} = \text{Orange Juice} + \text{Pineapple Juice} + \text{Lemon Lime Soda}
$$
$$
\text{Total Punch} = 16 \text{ cups} + 6 \text{ cups} + 8 \text{ cups} = 30 \text{ cups}
$$

### Step 3: Determine how many guests can be served
Each guest is served 2 cups of punch. Therefore, the number of guests that can be served is:
$$
\text{Number of Guests} = \frac{\text{Total Punch}}{\text{Punch per Guest}} = \frac{30 \text{ cups}}{2 \text{ cups/guest}} = 15 \text{ guests}
$$

### Step 4: Calculate how much punch will be left
Since Mr. Hernandez can serve 15 guests, the total amount of punch consumed will be:
$$
\text{Punch Consumed} = \text{Number of Guests} \times \text{Punch per Guest} = 15 \text{ guests} \times 2 \text{ cups/guest} = 30 \text{ cups}
$$
Since he has 30 cups of punch and serves all of it, there will be:
$$
\text{Punch Left} = \text{Total Punch} - \text{Punch Consumed} = 30 \text{ cups} - 30 \text{ cups} = 0 \text{ cups}
$$

### Final Answer
- Mr. Hernandez can serve **15 guests**.
- There will be **0 cups of punch left**.
Mr. Hernandez can serve 15 guests, and there will be no punch left.

Mr. Hernandez combines 1 gallon of orange juice, 3 pints of pineapple juice, and 2 quarts of lemon lime soda to make punch for a party. He allows 2 cups of punch for each guest. How many guests can he serve? How much punch will be left?

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