Boyle's Law Problem 1

$\displaystyle P \propto \frac{1}{V}$ only when the right hand side of the Ideal Gas Equation is constant.

In other words,
Since $\displaystyle PV=nRT$ , then,

For $\displaystyle P\propto \frac{1}{V}$ , we want,

$\displaystyle nRT = K$

Thus,
Assuming the Temp. doesn't change,
$\displaystyle n =$ no. of moles $\displaystyle = K$

But, while blowing air into the balloon, we increase the quantity of air inside it, and therefore, $\displaystyle n$ is not constant, i.e the mass of the gas is not fixed.
This would lead us to think that Boyle's Law is violated.

Boyle's experiment held two parameters constant: the temperature of the gas and the number of moles of the gas. The scenario above is definitely one in which the number of moles increases significantly. Thus, it is inappropriate to use Boyle's Law here at all.