College Algebra word problem

Question

The heights of five mountain peeks are related as follows:

 

The height of mountain A is 65 feet more than half the height of mountain C.

 

The height of mountain B is 36 feet more than three times the height of mountain D.

 

The mountain C is 164 feet taller than mountain D.

 

The mountain E is 137 feet shorter than mountain D.

 

The sum of the five heights is 2641 feet.

 

Find the height of each of the five structures:

Height of mountain A=_________ feet

Height of mountain B=_________ feet

Height of mountain C=_________ feet

Height of mountain D=_________ feet

Height of mountain E=_________ feet

 

 

Answer 1

A,B,C,D,E are the height of mountain A,B,C,D,E respectively.

 

A=65+0.5C

B=36+3D

C=164+D  --> D=C-164

E=D-137=C-164-137=C-301

A+B+C+D+E = 2641 --- (1)

 

Substitute A,B,D and E into (1)

(65+0.5C) + [36+3*(C-164)] + C + (C-164) +(C-301) = 2641

C = 538 feet

All other value follows.