SOLUTION: Julio Mendez is a carpenter. He is building a staircase between the first and second floors of a house, a height of 9 feet. The tread, or depth of each step, must be 10 inches. The

Algebra ->  Linear-equations -> SOLUTION: Julio Mendez is a carpenter. He is building a staircase between the first and second floors of a house, a height of 9 feet. The tread, or depth of each step, must be 10 inches. The      Log On


   

Question 64985This question is from textbook Glencoe Algebra 1
: Julio Mendez is a carpenter. He is building a staircase between the first and second floors of a house, a height of 9 feet. The tread, or depth of each step, must be 10 inches. The slope of the staircase cannot exceed 3/4.
How many steps should he plan? This question is from textbook Glencoe Algebra 1

Answer by cristiana(10) About Me  (Show Source):
You can put this solution on YOUR website!
Let's choose the working unit to be inches; therefore, height = 9 feet = 108 inches
Let x be the number of stairs. Each stair has a depth = 10 inches. We can therefore say that the horizontal length = 10*x
Slope = 3/4 = (y2-y1)/(x2-x1) = 108/10x.
If we solve for x: x=14.45
In order to see whether we need 14 or 15 stairs we need to try calculate the slope for both cases.
x = 14 implies slope=108/10*14=0.77
x = 15 implies slope=108/10*15=0.72
We know that the slope should not exceed 3/4=0.75 and therefore we choose x=15 no of steps.

Cristiana