# Volume of 0.5 M HCl needed to make a 10 % 500 ml solution

What volume of $$0.5\ \mathrm M$$ HCl solution is needed to prepare a $$500\ \mathrm{ml}$$ $$10\ \%$$ concentration solution, whose density is $$1.05\ \mathrm{g/cm^3}$$.

I've started off with finding the mass of the final solution, which would be $$500\ \mathrm{cm^3} \times 1.05\ \mathrm{g/cm^3} = 525\ \mathrm g$$. Next I find the mass of the HCl in it, $$52.5\ \mathrm g$$. After that, the moles of HCl, approx. $$1.4384\ \mathrm{mol}$$.

But after that I'm not sure how to proceed. I've tried dividing the molarity by the moles to get the volume, but that didn't work. I think I might have to make a system of equations but I'm bad at math so if that's how it's supposed to be done, I'd like for someone to show me how.