Let's solve the problem together.

Problem Summary:

• Maverick has twice as many apples as his friend.
• Together, they have 45 apples.
• If Maverick gives $x$ apples to his friend, he will have 5 more apples than his friend.
• We need to find the number of apples $x$ that Maverick gave to his friend.

Step-by-Step Solution:

1. Define Variables:

   • Let $F$ be the number of apples Maverick's friend has.
   • Then, Maverick has $2F$ apples since he has twice as many as his friend.

2. Formulate the Equations:

   • The total number of apples is: $F + 2F = 45$ Simplifying: $3F = 45$ $F = \frac{45}{3} = 15$ So, Maverick's friend has 15 apples, and Maverick has $2 \times 15 = 30$ apples.

3. Analyze the Transfer Condition:

   • After Maverick gives $x$ apples to his friend, Maverick will have $30 - x$ apples, and his friend will have $15 + x$ apples.
   • According to the problem, after this transfer, Maverick will have 5 more apples than his friend: $30 - x = (15 + x) + 5$

4. Solve the Equation:

   • Simplify and solve the equation: $30 - x = 20 + x$ $30 - 20 = x + x$ $10 = 2x$ $x = \frac{10}{2} = 5$

Conclusion:

Maverick gave 5 apples to his friend.

Would you like more details on any part of this solution? Here are some follow-up questions for further exploration:

1. How many apples does each person have after the exchange?
2. What if the total number of apples was 60 instead of 45?
3. What would happen if Maverick initially had three times as many apples as his friend?
4. How would the problem change if they had 50 apples together instead of 45?
5. What if Maverick wanted to have 10 more apples than his friend after giving some apples?

Tip: When dealing with algebraic word problems, defining variables clearly and setting up equations based on the conditions given is crucial for finding the solution.