Question

1. julie wants to rearrange the square tables and seats at the restaurant to make one big rectangular table. - there are 5 square tables. - each square table can have 4 seats. a. complete the table. | number of square tables | total number of seats | | --- | --- | | 1 | | | 2 | | | 3 | | | 4 | | | 5 | | | t | | b. how many seats can fit around 20 square tables pushed together to form one rectangular table? use the expression you wrote in the last row of the table in part (a). c. how many seats can fit around 50 square tables pushed together to form one rectangular table? use the expression you wrote in the last row of the table in part (a).

Explanation:

Step1: Find seats for 1 table

A single square table has 4 seats.

Step2: Find seats for 2 tables

When 2 square tables are pushed together, 2 seats are shared, so total seats = $4+4-2=6$

Step3: Find seats for 3 tables

Each added table adds 2 seats: $6+2=8$

Step4: Find seats for 4 tables

Add 2 more seats: $8+2=10$

Step5: Find seats for 5 tables

Add 2 more seats: $10+2=12$

Step6: Derive general formula

For $t$ tables, the number of seats is $2t+2$ (since 1 table has 4 seats = $2(1)+2$, and each extra table adds 2)

Step7: Calculate seats for 20 tables

Substitute $t=20$ into $2t+2$: $2(20)+2=40+2=42$

Step8: Calculate seats for 50 tables

Substitute $t=50$ into $2t+2$: $2(50)+2=100+2=102$

Answer:

Part (a)

Number of Square Tables	Total Number of Seats
2	6
3	8
4	10
5	12
$t$	$2t+2$

Part (b)

42

Part (c)

102