Questions: Mike and El are a couple, but El is moving to a different state. They assign 100 total points to items they have collected over their relationship. El Mike -------------- Waffles 40 25 Games 30 45 T-shirts 30 30 In the first step of the Adjusted Winner Procedure, start by giving each item to the person who gave it the most points. In the case of tie, whoever won fewer points gets it. Who gets the T-shirts?

Solution Steps

To determine who gets the T-shirts using the Adjusted Winner Procedure, we first compare the points assigned by El and Mike to each item. The T-shirts have equal points from both El and Mike. Since it's a tie, we give the T-shirts to the person who has won fewer points from the other items.

We have the following points assigned by El and Mike for each item:

• Waffles: \( E_W = 40 \), \( M_W = 25 \)
• Games: \( E_G = 30 \), \( M_G = 45 \)
• T-shirts: \( E_T = 30 \), \( M_T = 30 \)

We allocate each item to the person who assigned the most points. For the items:

• Waffles: \( E_W > M_W \) implies El gets Waffles.
• Games: \( M_G > E_G \) implies Mike gets Games.
• T-shirts: \( E_T = M_T \) is a tie, so we need to consider total points to decide.

Thus, the initial allocation is:

• Waffles: El
• Games: Mike

Next, we calculate the total points for each person based on the initial allocation:

• Total points for El: \[ E_{\text{total}} = E_W = 40 \]

• Total points for Mike: \[ M_{\text{total}} = M_G = 45 \]

Since the T-shirts are tied, we allocate them to the person with fewer total points. Here, \( E_{\text{total}} = 40 < M_{\text{total}} = 45 \), so El receives the T-shirts.

Final Answer