SOLUTION: The Sears Tower in Chicago is 1,450 feet tall, which is 1 4/25 times as tall as the Empire State Building in New York City. How tall is the Empire State Building. The easy wa

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: The Sears Tower in Chicago is 1,450 feet tall, which is 1 4/25 times as tall as the Empire State Building in New York City. How tall is the Empire State Building. The easy wa      Log On


   

Question 399068: The Sears Tower in Chicago is 1,450 feet tall, which is 1 4/25 times as tall as the Empire State Building in New York City. How tall is the Empire State Building.
The easy way to answer this is to Google it, but I have to show my work using a variable.
Answer by JoeCollins(4) About Me  (Show Source):
You can put this solution on YOUR website!
The question is asking for the height of the Empire State Building. Since that's the unknown, we will use a variable x to describe it. The question states that the Sears Tower is 1 4/25 times the height of the Empire State Building. So a pseudo-equation would be (Height of Sears Tower) = 1 4/25 x (Height of Empire State Building. Placing 1,450 for the Sears Tower and x for the Empire State Building yields the equation:
1450=%281%2B4%2F25%29%2Ax
Then it's just a matter of solving for x:
1450=%2825%2F25%29%2B%284%2F25%29%2Ax *Convert 1 to 25/25 so we can add it to 4/25.

1450=%2829%2F25%29%2Ax *Add the two fractions, to get 29/25.

%2825%29%2A1450=%2829%29%2Ax *Multiply both sides by 25, and

%2825%2A1450%29%2F29=x divide both sides by 29, to isolate x.

So, x=%2825%2A1450%29%2F29
And further calculation yields x, the height of the Empire State Building, is 1250 ft.