A restaurant uses 2 tables for 10 people, 3 tables for 15 people, and 4 tables for 20 people. Using the same relation, 7 tables are needed for 35 people. This is a case where it is... A restaurant uses 2 tables for 10 people, 3 tables for 15 people, and 4 tables for 20 people. Using the same relation, 7 tables are needed for 35 people. This is a case where it is represented by a straight line that passes through. Read more

Steps to Solve

1. Identify Table and People Ratio
   Examine the given data:

   • 2 tables accommodate 10 people: $\frac{10}{2} = 5$ \text{ people per table}
   • 3 tables accommodate 15 people: $\frac{15}{3} = 5$ \text{ people per table}
   • 4 tables accommodate 20 people: $\frac{20}{4} = 5$ \text{ people per table}

   The ratio of people per table is consistent: 5 people per table.

2. Calculate for 35 People
   To determine if the pattern holds for 35 people, use the same ratio:
   Number of tables required is given by:
   $$ \text{Tables needed} = \frac{\text{Number of people}}{\text{People per table}} = \frac{35}{5} = 7 $$

3. Determine Relationship Type
   Since the number of tables used directly corresponds to the number of people at a constant ratio, this indicates a proportional relationship, meaning:

   • If you increase the number of people, the number of tables increases in a linear fashion.