A company supplies tables for business meetings. Each table is a rectangle, and

Question

A company supplies tables for business meetings. Each table is a rectangle, and can seat one person on its short edge, and two people on its long edge, like the figures on the right. The diagrams below show how these tables can be made into arrangements for different numbers of people. The different arrangements are numbered, like the figures below. No one sits inside the arrangements of tables. How many people can sit at a Size 3 arrangement? How many people can sit around a Size 13 arrangement? Explain how you know your answer is correct. Write an equation for the number of people p who can sit at a Size S arrangement. Explain how the parts of your equation relate to the table arrangements. James is trying to seat 75 people. What size arrangement will he need? Write an explanation that would convince a classmate your answer is correct.

Explanation / Answer

1) Total number of people can sit = 2* total number of tables + 4 (corners seat)

for size 3 i.e. total 8 tables = 2*8 + 4 = 20 people

2) for size 13 i.e. 2*13 +2 = 28 tables

total number of people = 2*28 +4 = 60 people

3) Size S and no of tables T and total number of people p

T =2 S + 2

P = 2 T + 4

P = 2(2S+2) +4

P = 4S +8

4) 75 =4S +8

4S = 67

S =17 i.e. 36 Tables for 75 people

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