Question

Read the following description of a relationship:
Tom has a collection of 9 superhero lunch boxes. He decides he'll buy one new lunch box every year for his birthday.
Let y represent the number of years from now and b represent the total number of lunch boxes in Tom's collection.
This relationship can also be shown in a table. Complete the equation that represents the relationship between y and b.
y b
5 14
6 15
7 16
8 17

Answer 1

To determine the equation that represents the relationship between \( y \) (the number of years from now) and \( b \) (the total number of lunch boxes in Tom's collection), we can observe the data in the table you provided:

- When \( y = 5 \), \( b = 14 \)
- When \( y = 6 \), \( b = 15 \)
- When \( y = 7 \), \( b = 16 \)
- When \( y = 8 \), \( b = 17 \)

From these values, we can see that the total number of lunch boxes (\( b \)) increases by 1 for each additional year (\( y \)).

Given that Tom starts with 9 lunch boxes:

1. We can express the total number of lunch boxes after \( y \) years as:
\[
b = 9 + y
\]

Now, let's calculate the values to verify:

- For \( y = 5 \):
\[
b = 9 + 5 = 14
\]

- For \( y = 6 \):
\[
b = 9 + 6 = 15
\]

- For \( y = 7 \):
\[
b = 9 + 7 = 16
\]

- For \( y = 8 \):
\[
b = 9 + 8 = 17
\]

The equation \( b = 9 + y \) matches all observations in the table.

Thus, the complete equation representing the relationship between \( y \) and \( b \) is:
\[
b = 9 + y
\]