Question

Bill has his hats. If he buys eight more hats and then multiplies his total by three, he would still have fewer hats than Jim. Jim has 45 hats. How many hats does Bill have?

Answer 1

To determine how many hats Bill currently has, we set up an inequality with the given conditions and solved for the initial number of hats. Bill has 6 or fewer hats before purchasing the additional eight.

Step-by-step explanation:

Let's find out how many hats Bill currently has before making the purchase. According to the student's question, we know that if Bill buys eight more hats and then multiplies his total number of hats by three, he would still have fewer hats than Jim, who has 45 hats. Mathematically, we can set up the following inequality to represent the scenario:

(Initial number of hats + 8) × 3 < 45.

Let's call the initial number of hats Bill has 'B'. Then the inequality becomes:

(B + 8) × 3 < 45

Now, we divide both sides of the inequality by 3 to isolate B:

B + 8 < 45 / 3

B + 8 < 15.

Subtracting 8 from both sides of the inequality gives us:

B < 15 - 8

B < 7.

Since Bill can't have a fraction of a hat, we conclude that Bill has 6 or fewer hats before the purchase.