The average height of mountain A is 19436 ​ft, and its average height is 8870 ft less than the sum of the average heights of mountains B and C

Question

The average height of mountain A is 19436 ft, and its average height is 8870 ft less than the sum of the average heights of mountains B and C. The average height of mountain C is 272 ft less than four-sevenths of the average height of mountain B. Find the average height of mountain C.
The average height of mountain C is ______ ft.

Answer 1

Hello Dallas

 

Let's first break down the question into separate algebraic equations.

 

1) The average height of mountain A is 19436 ft;  (A = 19436)

 

2) .... and its average height is 8870 ft less than the sum of the average heights of mountains B and C;  A = (B+C) - 8870

 

3) The average height of mountain C is 272 ft less than four-sevenths of the average height of mountain B;  C = 4/7 B - 272

 

Starting with equation 2,

 

A = (B+C) - 8870

 

Substitute A = 19436 in the above equation, you get

 

19436 = (B+C) - 8870

 

(B+C) = 19436 + 8870 = 28306

 

Equation 3 is

 

C = 4/7 B - 272

 

Rearrange to solve for B

 

4/7 B = (C+272)

 

B = 7/4 (C+272)

 

Substitute B = 7/4 (C+272) into (B+C) = 28306

 

7/4 (C+272) + C = 28306

 

7/4 C + 476 + C = 28306

 

7/4 C + C = (28306 - 476)

 

11/4 C = 27830

 

Solving for C,

 

C = 4 /11 x 27830 = 10120 ft