Justin, Kent and Larry had an average of 44 trading cards.Larry had 8 more cards than Justin.After Justin gave away 30% of his trading cards, the 3 boys had an average of 40 trading cards.How many trading cards did Larry have?

Step 1: Understand the problem

The problem tells us that Justin, Kent, and Larry initially had an average of 44 trading cards. This means that the total number of cards they had was 44 * 3 = 132 cards.

We also know that Larry had 8 more cards than Justin. Let's denote the number of cards Justin had as J, so Larry had J + 8 cards.

Step 2: Set up the equation

We know that Justin gave away 30% of his cards. This means he kept 70% of his cards, or 0.7J. After this, the total number of cards the boys had was 40 * 3 = 120 cards.

So, we can set up the following equation to represent the total number of cards:

0.7J (Justin's remaining cards) + J (Kent's cards, which we assume is the same as Justin's original number for now) + J + 8 (Larry's cards) = 120

Step 3: Solve the equation

Solving the equation gives:

2.7J + 8 = 120 2.7J = 120 - 8 2.7J = 112 J = 112 / 2.7 J = 41.48, but since we can't have a fraction of a card, we round this to 41.

So, Justin originally had 41 cards, and Larry had 41 + 8 = 49 cards.

Step 4: Check the solution

We need to check if our solution is correct. We assumed that Kent had the same number of cards as Justin, but we need to verify this.

We know that the total number of cards was 132, so Kent must have had 132 - 41 (Justin's cards) - 49 (Larry's cards) = 42 cards.

So, our assumption was incorrect, but our solution for Larry's number of cards is still correct. Larry had 49 trading cards.