At a child's lemonade stand, p pitchers of lemonade are made by adding m packets of lemonade mix to cold water. If `m =2p +4,` how many more packets of lemonde mix are needed to make each additional pitcher of lemonade ?

Options

A. 0
B. 1
C. 2
D. 4

Explanation

To solve the problem step by step, we need to determine how many additional packets of lemonade mix are needed for each additional pitcher of lemonade.

### Step 1: Understand the relationship between pitchers and packets
We are given that the number of packets of lemonade mix \( m \) needed for \( p \) pitchers is given by the equation:
\[ m = 2p + 4 \]

### Step 2: Calculate the packets needed for \( p \) pitchers
Using the formula, for \( p \) pitchers, the number of packets needed is:
\[ m = 2p + 4 \]

### Step 3: Calculate the packets needed for \( p + 1 \) pitchers
Now, we need to find out how many packets are needed for \( p + 1 \) pitchers. We substitute \( p + 1 \) into the formula:
\[ m = 2(p + 1) + 4 \]
This simplifies to:
\[ m = 2p + 2 + 4 = 2p + 6 \]

### Step 4: Determine the difference in packets between \( p + 1 \) and \( p \)
Now we need to find out how many more packets are needed when going from \( p \) pitchers to \( p + 1 \) pitchers. We subtract the number of packets needed for \( p \) pitchers from the number needed for \( p + 1 \) pitchers:
\[ (2p + 6) - (2p + 4) \]

### Step 5: Simplify the expression
Now, simplify the expression:
\[ (2p + 6) - (2p + 4) = 2p + 6 - 2p - 4 = 2 \]

### Conclusion
Thus, the number of additional packets of lemonade mix needed to make each additional pitcher of lemonade is:
\[ \boxed{2} \]