Question
Read the following description of a relationship:
Each relay team entered in a middle school track meet has 7 runners.
Let t represent the number of teams and r represent the total number of runners.
This relationship can also be shown in a table. Complete the equation that represents the relationship between t and r.
t r
7 49
8 56
9 63
10 70
r=
Each relay team entered in a middle school track meet has 7 runners.
Let t represent the number of teams and r represent the total number of runners.
This relationship can also be shown in a table. Complete the equation that represents the relationship between t and r.
t r
7 49
8 56
9 63
10 70
r=
Answers
Answered by
GPT-4o mini
To determine the equation that represents the relationship between \( t \) (the number of teams) and \( r \) (the total number of runners), we can observe the data given in the table:
For each team, there are 7 runners. Therefore, the total number of runners \( r \) can be expressed in terms of the number of teams \( t \) as:
\[
r = 7t
\]
We can verify this with the values from the table provided:
- For \( t = 7 \): \( r = 7 \times 7 = 49 \)
- For \( t = 8 \): \( r = 7 \times 8 = 56 \)
- For \( t = 9 \): \( r = 7 \times 9 = 63 \)
- For \( t = 10 \): \( r = 7 \times 10 = 70 \)
All these calculations confirm that the equation is indeed correct.
Thus, the final equation representing the relationship between \( t \) and \( r \) is:
\[
r = 7t
\]
For each team, there are 7 runners. Therefore, the total number of runners \( r \) can be expressed in terms of the number of teams \( t \) as:
\[
r = 7t
\]
We can verify this with the values from the table provided:
- For \( t = 7 \): \( r = 7 \times 7 = 49 \)
- For \( t = 8 \): \( r = 7 \times 8 = 56 \)
- For \( t = 9 \): \( r = 7 \times 9 = 63 \)
- For \( t = 10 \): \( r = 7 \times 10 = 70 \)
All these calculations confirm that the equation is indeed correct.
Thus, the final equation representing the relationship between \( t \) and \( r \) is:
\[
r = 7t
\]