Math problem involving linking patterns, formulas, tables, and graphs to determine the number of chairs needed for different numbers of tables in a cafe setting.

- (a) Complete the table below:
- Tables: 1, Chairs Needed: 4
- Tables: 2, Chairs Needed: 6
- Tables: 3, Chairs Needed: 8
- Tables: 4, Chairs Needed: 10
- Tables: 5, Chairs Needed: 12

- (b) Complete the formula:
- Chairs Needed = 2 x Tables + 2

- (c) Use the formula to find the number of chairs required for:
- (i) 8 tables: 18
- (ii) 12 tables: 26
- (iii) 1000 tables: 2002

- (d) Use the formula to find the number of chairs required for 0 tables. Does this make sense in the context?
- For 0 tables, the formula gives 2 chairs. This does not make practical sense, as no tables would mean no chairs are needed.

- (e) Use your table to plot points on the set of axes.
- Plot the points: (1,4), (2,6), (3,8), (4,10), (5,12)

- (f) Join up the points with a straight line.
- Draw a straight line through the plotted points.

- (g) Extend your line in both directions. Can you spot the answer to question d on the graph?
- Extending the line to the left intersects the y-axis at (0,2), which corresponds to the answer from part (d).

- (h) Will a situation ever arise which requires 41 tables?
- No, because the number of chairs is always even (2 × Tables + 2), and 41 is odd. Therefore, 41 chairs cannot be required for any number of tables under this arrangement.