Question

If a varies directly with b, and a=8 when b=20, what is the value of a when b=14.5?

Answer 1

Since we know that a varies directry with b, this means that

`(a)/(b)=k`

where k is a proportional constant.

If we plugg in the values we have we can find k. Then

`\begin{gathered} k=(8)/(20) \\ =(2)/(5) \end{gathered}`

Therefore, in our case

`(a)/(b)=(2)/(5)`

Now we want to know the value of a when b=14.5, plugging the value in the last equation we have

`(a)/(14.5)=(2)/(5)`

Now we solve for a

`\begin{gathered} (a)/(14.5)=(2)/(5) \\ a=(2)/(5)\cdot14.5 \\ a=2.8 \end{gathered}`

Therefore, when b=14.5 than a=2.8.