Question

a restaurant has 30 tables in its dining room. it takes a waiter 10 minutes to set 8 tables. at this rate, how long will it take the waiter to set all the tables in the dining room? now find another equivalent ratio. how long will it take to set 24 tables? | minutes | tables | | --- | --- | | 10 | 8 | |? | 30 | | 20 | 16 | | | 24 |

Explanation:

Part 1: Time to set 30 tables

Step1: Find the rate per table

The waiter takes 10 minutes to set 8 tables. So the time per table is the total time divided by the number of tables. The rate (time per table) is $\frac{10}{8}$ minutes per table.

Step2: Calculate time for 30 tables

To find the time for 30 tables, multiply the rate per table by 30. So time $= \frac{10}{8} \times 30$. Simplify $\frac{10}{8}=\frac{5}{4}$, then $\frac{5}{4} \times 30=\frac{150}{4} = 37.5$ minutes.

Step1: Use the rate from before

The rate is still $\frac{10}{8}$ minutes per table (or we can see the pattern from the table: 8 tables take 10 minutes, 16 tables take 20 minutes, so it's a proportional relationship).

Step2: Set up proportion or use rate

Using the rate $\frac{10}{8}$ minutes per table, for 24 tables, time $=\frac{10}{8} \times 24$. Simplify: $\frac{10}{8} \times 24 = 10\times3 = 30$ minutes (since 24 divided by 8 is 3, and 10 times 3 is 30).

Answer:

37.5 minutes

Part 2: Time to set 24 tables