building height problem

Question

The federal building is as much taller than the state building as the state building is taller than the city building. If federal building is 160 ft tall and city is 80 ft tall. How tall is state building

Answer 1

the difference between the height of the federal and the state is the same as the difference between the state and the city

 

seeing that these are the conditions, the state must be in the middle of the federal and the city

 

160-80=80, 80/2=40

 

160-40=120 feet for the state

 

 

Answer 2

Let's define a few variables.

 

F = height of Federal Building

S = height of State Building

C = height of City Building

 

From the problem we know that the difference between the height of the federal building and the height of the state building is the same as the difference between the height of the state building and the city building.  We also know that the heights of the buildings from tallest to shortest can be written as F>S>C.

 

So, written algebraically,

 

F - S = S - C

 

Given that F = 160 and C = 80,

160 - S = S - 80

 

Rearranging terms

240 = 2S

 

and

S = 120

 

So the State Building is 120 feet tall.

 

Also note that F-S = 160 - 120 = 40.  

And S-C = 120-80 = 40.

Answer 3

 

Let x = "as much taller than" or "How much taller?"

 

Translate:

  "federal building is as much taller than the state building"     means

             F            =          x                +              S                           [eq1]

  "state building is taller than the city building      means

            S          =         x   +          C                                         [eq2]

  "is as ... as"   tells us that the x value is the same in each equation

 

Now, the math:

    F = 160                 [given]

    C = 80                  [given]

 

     160 = x + S                    [from eq1 and value of F]]

     160 = x + (x+80)            [use eq2 and value of C]

     160 = 2x + 80

      80 = 2x                    [subtract 80 from both sides]

      40 = x                    [divide both sides by 2]

 

"How tall is state building?"
    S = x + C              or     F = x + S                [note: use either eq1 or eq2]
    S = 40 + 80          or      160 = 40 + S
    S = 120               or        S = 120                 [both methods work!]