Objective: Compare step measurements to see how they affect stairway design. Learning Goals: - Calculated the slope of a stairway - Write linear inequalities in two variables - Graph systems of linear inequalities - Interpret the shaded solution area of a system in the context in real life. 1) Investigating the data: Complete #1-6 under this category. The horizontal part of a step is the tread, and the vertical part is the riser. The table gives the tread and riser measurements of four different stairways. Stairway Tread (in.) Riser (in.) A 10 7 B 11 7 C 9 8 D 12 6

#1. Use the measurement in the table to draw three steps for each Stairway A- D on a piece of graph paper. Don't forget to include the key for the measurement. #2. Analyze your drawings. Which stairway is the steepest? Which stairway gives the most foot space on a step? #3. For each Stairway A-D, find the ratio of riser size to tread size . Then write each ratio as a decimal rounded to the nearest tenth. What characteristic of a stairway do these ratios describe? Two generally accepted rules for designing stairways are listed below. Rule 1: The sum of one tread and one riser is from 17 inches to 18 inches. Rule 2: The sum of one tread and two risers is from 24 inches to 25 inches. #4. You can use the following linear inequalities to represent Rule 1.

Write linear inequalities to represent Rule 2. Then use the inequalities to show that each Stairway A-D follows one of the rules. #5. Graph the system of four inequalities on the same coordinate plane. Use the horizontal axis for t and the vertical axis for r. Then use the values in the table to label the point (t, r) for each Stairway A-D. What does each solution of the system represent? #6. Name any other point E that is the solution of the system. Give tread and riser measurements for a Stairway E that the point represents.

--> Please solve only question #5 using the data above. Thank you

#4: Writing Linear Inequalities

Rule #1 :18 t + r 17 Rule #2: 25 t + 2r 24

Staircase	Rule	Inequality
Staircase A	Rule #1	18 17 17 Tread = 10 Rise = 7(7+10)
Staircase B	Rule #2	25 25 24 Tread = 11 Rise = 7(11 + 2 x 7)
Staircase C	Rule #1	18 17 17 Tread = 9 Rise = 8(9+8)
Staircase D	Rule #2	25 24 24 Tread = 12 Rise = 6(12 + 2 x 6)

Based on this table, the staircases rise and treads match with the rules inequalities