Question

If a is directly proportional to b, and a = 25 when b = 35, find b when a = 40

Answer 1

If a is directly proportional to b, we have the relationship to be:

`\begin{gathered} a\propto b \\ \therefore \\ a=kb \\ where \\ b=constant \end{gathered}`

When a = 25, b = 35. Therefore, we can calculate the value of k as follows:

`\begin{gathered} 25=35k \\ k=(25)/(35) \\ k=(5)/(7) \end{gathered}`

Therefore, the relationship is given to be:

`a=(5)/(7)b`

When a = 40, we can calculate the value of b to be:

`\begin{gathered} 40=(5)/(7)b \\ 40*7=5b \\ 5b=280 \\ b=(280)/(5) \\ b=56 \end{gathered}`

The value of b is 56.