College Algebra- Word Problem

Question

The average height of mountain A is 19,210 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 280 ft less than four-sevenths of the average height of mountain B. Find the average height of mountain C.

Answer 1

The information is given in reverse order from the way it is used.

 

B represents the height of mountain B

4B/7 - 280 represents the height of mountain C

B + 4B/7 - 280 - 8890 represents the height of mountain A

 

19210 = B + 4B/7 - 280 - 8890   combine like terms

19210 = 11B/7 - 9170                 add 9170 to both sides

28380 = 11B/7                            multiply both sides by 7

198660 = 11B                             divide both sides by 11

18060 = B

 

Now you can calculate the height of mountain C.

Answer 2

Let average height of mountain A = A

Let average height of mountain B = B

Let average height of mountain C = C

 

 

Use these variables to write equations that represents the description.

 

A = 19210                         eq1

 

B + C - 8890 = A                eq2

 

(4/7)B - 280 = C                 eq3

 

 

Since we know A, we can plug in A into eq2.

 

B + C - 8890 = 19210 

 

B + C = 28100

 

 

Now we have one less equation to deal with.  All that is left is

 

B + C = 28100                             eq2

(4/7)B - 280 = C                          eq3

 

 

Substitute eq2 into eq3.  This will give us only one equation in terms of C.

 

(4 / 7)(28100 - C) - 280 = C

 

 

Use this newly single equation to solve for C.  I leave this part to you.