Let's carefully analyze the given problem step by step:
1. Understand the Initial Setup:
- Initially, there are 40 coins divided evenly among four friends.
- Each friend starts with [tex]\(\frac{40}{4} = 10\)[/tex] coins.
2. Distribution of Coins:
- Each player keeps 2 coins on the table.
- Therefore, the number of coins each player has left in their bag is [tex]\(10 - 2 = 8\)[/tex] coins. Let [tex]\(b\)[/tex] represent the number of coins in each bag, so [tex]\(b = 8\)[/tex].
3. Coin Distribution in Terms of Equation:
- The two coins on the table are accounted for, so each player has [tex]\(b\)[/tex] coins in their bag.
- Together, the number of coins each player possesses, combining both their bag and the table, is [tex]\(b + 2\)[/tex].
4. Total Number of Coins:
- To find the total number of coins all four players have considering our [tex]\(b\)[/tex] value, we need to multiply the full set of coins each player has (coins in bag and coins on the table) by 4 (since there are four players):
[tex]\[
4 \times (b + 2)
\][/tex]
5. Total Coin Equation:
- We know from the setup that the game begins with 40 coins in total. Hence we equate it to our previous calculation:
[tex]\[
4(b + 2) = 40
\][/tex]
6. Verification:
- Verify if our variables and constants match up correctly:
- Given [tex]\(b = 8\)[/tex], we replace [tex]\(b\)[/tex] in the equation [tex]\(4(b + 2) = 40\)[/tex]:
[tex]\[
4(8 + 2) = 4 \times 10 = 40
\][/tex]
- This confirms our equation is consistent and valid.
Therefore, the equation that represents the total number of coins the four players have is:
[tex]\[
4(b + 2) = 40
\][/tex]
