Question

if b varies jointly with a and c and b = 112 when a = 12 and c = 7, find a when b = 72 and c = 2

Answer 1

Given:

b jointly varies with a and c. This can be written as,

$b=kac$

where k is a constant.

We need to determine the value of a when b = 72 and c = 2

Value of k:

Also, given that the value b = 112 when a = 12 and c = 7.

Hence, substituting these values in the expression $b=kac$, we get;

$112=k(12)(7)$

$112=84k$

  $\frac{4}{3}=k$

Thus, the value of k is $k=\frac{4}{3}$

Value of a:

The value of a can be determined by substituting b = 72, c = 2 and $k=\frac{4}{3}$ in the expression $b=kac$, we have;

      $72=\frac{4}{3}a(2)$

      $72=\frac{8}{3}a$

$72\times \frac{3}{8}=a$

       $9=a$

Therefore, the value of a is 9.