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 $60\%$ magical syrup by volume (and the rest is just water), and blue potion, which is $30\%$ magical syrup by volume.
Does there exist a combination of red potion and blue potion that can produce a potion that is $75\%$ magical syrup by volume?
Answer: Let the number of mL of 50% potion = FThen, the number of mL of 10% potion =200 - F 0.50F + 0.10[200 - F] =200 * 0.30, solve for F F = 100 mL of 50% potion will be needed.200 - 100 ==100 mL of 10% potion will be needed
