Suppose a varies jointly with b and c and inversely with d and a=400 when b=16, c=5 and d=2. write the equation that models the relationship. show all steps

For this item, we represent first the proportionality constant by the variable k. Being directly proportional to both b and c, these variable will be in numerator and d will be in the denominator. That is,
                                  a = kbc / d
Substituting the known values,
                                 400 = k(16)(5) / (2) 
The value of k is 10. The equation that models the relationship is therefore,
                                   a = 10bc/d