To find the unknown value representing the unit rate in the given proportional relationship between the number of boxes and the number of magnetic cubes, we need to determine the constant of proportionality.
From the table, we have the following pairs of values:
- 1 box corresponds to [tex]\( n \)[/tex] cubes.
- 5 boxes correspond to 625 cubes.
- 8 boxes correspond to 1000 cubes.
To find the constant of proportionality (unit rate), we can use the known values of 5 boxes and 625 cubes.
1. Set up the proportion:
The relationship is proportional, which means the number of cubes per box should be the same for each row.
[tex]\[
\text{Unit Rate} = \frac{\text{Number of cubes}}{\text{Number of boxes}}
\][/tex]
2. Use the given values of 5 boxes and 625 cubes:
[tex]\[
\text{Unit Rate} = \frac{625 \text{ cubes}}{5 \text{ boxes}}
\][/tex]
3. Calculate the unit rate:
[tex]\[
\text{Unit Rate} = 125 \text{ cubes per box}
\][/tex]
Therefore, the unit rate, which is the unknown value representing the constant of proportionality, is [tex]\( 125 \)[/tex].
