average height question

Question

The average height of mountain A is 19,306 ft, and its average height is 8890 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 - seventh of the average height of mountain B. Find the average height of mountain C.

Answer 1

What we know:

 

Height of mountain A

=> A= 19,306

 

Height of A is 8890 less than sum of B and C

=> 19,306=B+C-8890 

rearrange this to get an equation for B in terms of C

=> B=(19,306+8890)-C

B=28,196-C

 

Height of C is 272 less than 4/7 of B

=> C=4/7(B)-272

 

Substitute into this the equation for B we found above (B=28,196-C), rearrange and solve for C:

=> C=4/7(28,196-C)-272

C=16,112-4/7(C)-272

C+4/7(C)=16,112-272

7/7(C)+4/7(C)=15,840

11/7(C)=15,840

C=15,840*7/11

C=10,080

 

You can check this answer by substituting the value for C back into the original equations and ensure the values all check out.