Combined Variation Problem

Question

W is directly proportional to the square of L and inversely proportional to A. If W = 4 when L =2 and A = 10, find W when L =5 and A =20. 

Answer 1

k will be the constant of proportion

 

If W is directly proportional to the square of L

the generic equation is   W = kL²

 

If W is inversely proportional to A

the generic equation is W = k/A

 

Since W is directly proportional to L² and inversely

proportional to A the equation is:

 

W = kL²/A

 

Plugging in the given values of W, L, A to find k

 

4 = k(2²)/10

4 = 4k/10

40 = 4k

k =10

 

When L = 5 and A = 20 we have

 

W = 10(5²)/20

W = 250/20

W = 12.5 or 12 1/2