+1887 A magician makes potions by combining maple syrup from a magical maple tree with ordinary water. The magician starts with a large supply of two potions: a red potion, which is $50\%$ magical syrup by volume (and the rest is just water), and blue potion, which is $20\%$ magical syrup by volume. (Perhaps you're wondering how the same syrup can produce both red and blue potions. That's why it's magic syrup!)
(a) Find the amount of red potion (in mL) that must be added to $600$ mL of blue potion in order to produce potion that is $30\%$ magical syrup by volume.
(b) Find the amounts of red potion and blue potion (in mL) that can be combined in order to produce $150$ mL of a potion that is $42\%$ magical syrup by volume.
(c) Does there exist a combination of red potion and blue potion that can produce a potion that is $75\%$ magical syrup by volume?
