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:

$\begin{gathered} 25=35k \\ k=\frac{25}{35} \\ k=\frac{5}{7} \end{gathered}$

Therefore, the relationship is given to be:

$a=\frac{5}{7}b$

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

$\begin{gathered} 40=\frac{5}{7}b \\ 40\times7=5b \\ 5b=280 \\ b=\frac{280}{5} \\ b=56 \end{gathered}$

The value of b is 56.