An old factory chimney in Detroit is 50 feet lower than one in Chicago, and 1/3 of the height of the latter is 25 feet more than 1/4 of the height of the former

Question

This question is about buildings.

Answer 1

First, define the variables:

D = Detroit chimney height

C = Chicago chimney height

 

Next, find relationships between D and C:

"An old factory chimney in Detroit is 50 feet lower than one in Chicago"

D = C - 50

 

"1/3 of the height of the latter is 25 feet more than 1/4 of the height of the former"

(1/3)C = 25 + (1/4)D

 

Now, substitute the first expression for D into the second equation:

(1/3)C = 25 + (1/4)(C - 50)  (multiply both sides by common denominator 12 to eliminate fractions)

12(1/3)C = 12(25) + 12(1/4)(C - 50)  (cancel like factors in fractions)

4C = 300 + 3(C - 50)   (distribute on right)

4C = 300 + 3C - 150    (subtract 3C from both sides and combine like terms )

C = 150

 

Last, use C = 150 to find D:

D = C - 50 = 150 - 50 = 100

 

Solution: 

The Detroit chimney is 100 feet, and the Chicago chimney is 150 feet.

 

Check:

(1/3)150 = 50 = 25 + 25 = 25 + (1/4)100