A 2-column table with 4 rows. Column 1 is labeled Tickets purchased with entries 1, 2, 3, 4. Column 2 is labeled Entries with entries 3, 4, 5, 6.

Question

The table shows the number of carnival tickets purchased and the corresponding number of entries in the raffle drawing.

If x is the number of tickets purchased and y is the number of entries in the raffle drawing, then the equation
represents the table.
How many entries would be in the raffle drawing if 20 tickets were purchased?

Answer 1

Let's analyze the provided table:

| Tickets Purchased (x) | Entries (y) | |------------------------|-------------| | 1 | 3 | | 2 | 4 | | 3 | 5 | | 4 | 6 |

To find a relationship between the number of tickets purchased (x) and the number of raffle entries (y), we can observe the pattern in the table entries.

1. When 1 ticket is purchased, there are 3 entries.
2. When 2 tickets are purchased, there are 4 entries.
3. When 3 tickets are purchased, there are 5 entries.
4. When 4 tickets are purchased, there are 6 entries.

From this, we can deduce a linear relationship between x and y.

To find the equation, we note:

• The entries increase by 1 for each additional ticket purchased, starting from 3 when 1 ticket is purchased.

Based on this, we can express the relationship as: \[ y = x + 2 \]

Where:

• \( y \) is the number of entries,
• \( x \) is the number of tickets purchased.

Now, we need to check for \( x = 20 \): \[ y = 20 + 2 = 22 \]

Thus, if 20 tickets are purchased, there would be 22 entries in the raffle drawing.