
And in this problem, a would equal 3. Way to go if you got that one correct.

Since a varies inversely with b, we want to make sure that we put the b quantity

in the denominator. But for c, a varies directly with it. So we want to put that

straight across in the numerator. This is perhaps the trickiest part about

setting up variation problems. And you want to make sure you get it right each

time. Remember, with inverse relationships. They'll appear in opposite

positions, whereas with direct relationships, the variables will appear directly

across from one another. So in my first case, a is 12, b is three, and c is

eight. So I plug in those values. In the second case, we don't know the value of

a, so I leave that written as a in the denominator. But I do know that b2 is

equal to six. And c2 is equal to 4. These are the values of b and c in our

second case. Now that we have this equation, we multiply these two fractions

together to get 48 divided by 12. We cross multiply to get 144 equals 48a, and

finally we divide both sides by 48 to get a is equal to 3.