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

To find the relationship between the number of tickets purchased (\( x \)) and the number of entries in the raffle drawing (\( y \)), we can use the data provided in the table.

Let's analyze the entries from the table:

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

From the table, we can see that for each ticket purchased, the number of entries increases in a linear fashion.

• When \( x = 1 \), \( y = 3 \)
• When \( x = 2 \), \( y = 4 \)
• When \( x = 3 \), \( y = 5 \)
• When \( x = 4 \), \( y = 6 \)

Now, we notice that there is a consistent increase:

• For an increase of 1 ticket, there is an increase of 1 entry in the raffle drawing.

This suggests that the relationship can be expressed as: \[ y = x + 2 \]

This equation accounts for the offset where \( y \) equals \( 3 \) when \( x \) is \( 1 \).

Now, to find the number of entries when \( x = 20 \): \[ y = 20 + 2 \] \[ y = 22 \]

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