Jackie walks into a convenience store and recognizes the number of lottery tickets she can purchase varies inversely with the price of each ticket. If Jackie buys 5 tickets, she can purchase exactly 6 tickets. If she buys 3 tickets, what is the maximum number of tickets she can purchase? The solution is square

## Step 1: Identify the Relationship<br />### The problem states that the number of lottery tickets Jackie can purchase varies inversely with the price of each ticket. This means if \( x \) is the price per ticket and \( y \) is the number of tickets, then \( x \cdot y = k \), where \( k \) is a constant.<br />## Step 2: Calculate the Constant of Variation<br />### Given that when the price is \( \$5 \), Jackie can buy 6 tickets, we use the equation \( 5 \cdot 6 = k \). Solving this gives \( k = 30 \).<br />## Step 3: Determine the Number of Tickets for a Different Price<br />### Now, using the constant \( k = 30 \), we find the number of tickets Jackie can buy if the price is \( \$3 \). Using the equation \( 3 \cdot y = 30 \), solve for \( y \) to get \( y = 10 \).