:tSOLUTION
Step 1 :
In this question, we are told that the room is 15 feet tall.
An architect wants to include a window that is 6 feet tall.
The distance between the floor and the bottom of the window is b feet.
The distance between the ceiling and the top of the window is a feet.
This relationship can be described by the equation, a = 15 - (b + 6)
Step 2 :
From the above explanation, we can answer the following questions:
a) Which variable is independent based on the equation given?
The independent variable is b.
b) If the architect wants b to be 3, what does this mean?
What value of a, would work with the given value for b?
It means that the distance between the floor and the bottom of the window is 3 feet.
From the equation, a = 15 - ( b + 6 )
when b = 3 ,
a = 15 - ( 3 + 6 )
a = 15 - 9
a = 6
Therefore, the value of a = 6
It means that the distance between the ceiling and the top of the window is 6 feet.
Step 3 :
The customer wants the window to have 5 feet of space above it.
Is the customer describing a or b? What is the value of the other variable?
The customer is describing a .
When a = 5 .
Recall a = 15 - ( b + 6 )
5 = 15 - ( b + 6 )
b + 6 = 15 - 5
b + 6 = 10
collecting like terms, we have that :
b = 10 - 6
b = 4.